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COMPUTER SCIENCE (1172 journals)                  1 2 3 4 5 6 | Last

Showing 1 - 200 of 872 Journals sorted alphabetically
3D Printing and Additive Manufacturing     Full-text available via subscription   (Followers: 15)
Abakós     Open Access   (Followers: 4)
ACM Computing Surveys     Hybrid Journal   (Followers: 24)
ACM Journal on Computing and Cultural Heritage     Hybrid Journal   (Followers: 9)
ACM Journal on Emerging Technologies in Computing Systems     Hybrid Journal   (Followers: 13)
ACM Transactions on Accessible Computing (TACCESS)     Hybrid Journal   (Followers: 4)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 16)
ACM Transactions on Applied Perception (TAP)     Hybrid Journal   (Followers: 6)
ACM Transactions on Architecture and Code Optimization (TACO)     Hybrid Journal   (Followers: 9)
ACM Transactions on Autonomous and Adaptive Systems (TAAS)     Hybrid Journal   (Followers: 7)
ACM Transactions on Computation Theory (TOCT)     Hybrid Journal   (Followers: 12)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 3)
ACM Transactions on Computer Systems (TOCS)     Hybrid Journal   (Followers: 18)
ACM Transactions on Computer-Human Interaction     Hybrid Journal   (Followers: 15)
ACM Transactions on Computing Education (TOCE)     Hybrid Journal   (Followers: 6)
ACM Transactions on Design Automation of Electronic Systems (TODAES)     Hybrid Journal   (Followers: 2)
ACM Transactions on Economics and Computation     Hybrid Journal  
ACM Transactions on Embedded Computing Systems (TECS)     Hybrid Journal   (Followers: 4)
ACM Transactions on Information Systems (TOIS)     Hybrid Journal   (Followers: 21)
ACM Transactions on Intelligent Systems and Technology (TIST)     Hybrid Journal   (Followers: 8)
ACM Transactions on Interactive Intelligent Systems (TiiS)     Hybrid Journal   (Followers: 4)
ACM Transactions on Multimedia Computing, Communications, and Applications (TOMCCAP)     Hybrid Journal   (Followers: 10)
ACM Transactions on Reconfigurable Technology and Systems (TRETS)     Hybrid Journal   (Followers: 7)
ACM Transactions on Sensor Networks (TOSN)     Hybrid Journal   (Followers: 9)
ACM Transactions on Speech and Language Processing (TSLP)     Hybrid Journal   (Followers: 10)
ACM Transactions on Storage     Hybrid Journal  
ACS Applied Materials & Interfaces     Full-text available via subscription   (Followers: 25)
Acta Automatica Sinica     Full-text available via subscription   (Followers: 3)
Acta Universitatis Cibiniensis. Technical Series     Open Access  
Ad Hoc Networks     Hybrid Journal   (Followers: 11)
Adaptive Behavior     Hybrid Journal   (Followers: 11)
Advanced Engineering Materials     Hybrid Journal   (Followers: 26)
Advanced Science Letters     Full-text available via subscription   (Followers: 9)
Advances in Adaptive Data Analysis     Hybrid Journal   (Followers: 7)
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Advances in Remote Sensing     Open Access   (Followers: 40)
Advances in Science and Research (ASR)     Open Access   (Followers: 6)
Advances in Technology Innovation     Open Access   (Followers: 4)
AEU - International Journal of Electronics and Communications     Hybrid Journal   (Followers: 8)
African Journal of Information and Communication     Open Access   (Followers: 8)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 4)
Air, Soil & Water Research     Open Access   (Followers: 9)
AIS Transactions on Human-Computer Interaction     Open Access   (Followers: 6)
Algebras and Representation Theory     Hybrid Journal   (Followers: 1)
Algorithms     Open Access   (Followers: 11)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 5)
American Journal of Computational Mathematics     Open Access   (Followers: 4)
American Journal of Information Systems     Open Access   (Followers: 5)
American Journal of Sensor Technology     Open Access   (Followers: 4)
Anais da Academia Brasileira de Ciências     Open Access   (Followers: 2)
Analog Integrated Circuits and Signal Processing     Hybrid Journal   (Followers: 7)
Analysis in Theory and Applications     Hybrid Journal   (Followers: 1)
Animation Practice, Process & Production     Hybrid Journal   (Followers: 5)
Annals of Combinatorics     Hybrid Journal   (Followers: 3)
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Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 12)
Annals of Pure and Applied Logic     Open Access   (Followers: 2)
Annals of Software Engineering     Hybrid Journal   (Followers: 13)
Annual Reviews in Control     Hybrid Journal   (Followers: 6)
Anuario Americanista Europeo     Open Access  
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applied and Computational Harmonic Analysis     Full-text available via subscription   (Followers: 1)
Applied Artificial Intelligence: An International Journal     Hybrid Journal   (Followers: 13)
Applied Categorical Structures     Hybrid Journal   (Followers: 2)
Applied Clinical Informatics     Hybrid Journal   (Followers: 2)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 12)
Applied Computer Systems     Open Access   (Followers: 2)
Applied Informatics     Open Access  
Applied Mathematics and Computation     Hybrid Journal   (Followers: 33)
Applied Medical Informatics     Open Access   (Followers: 10)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Soft Computing     Hybrid Journal   (Followers: 15)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 5)
Architectural Theory Review     Hybrid Journal   (Followers: 3)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 5)
Archive of Numerical Software     Open Access  
Archives and Museum Informatics     Hybrid Journal   (Followers: 136)
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 4)
Artifact     Hybrid Journal   (Followers: 2)
Artificial Life     Hybrid Journal   (Followers: 7)
Asia Pacific Journal on Computational Engineering     Open Access  
Asia-Pacific Journal of Information Technology and Multimedia     Open Access   (Followers: 1)
Asian Journal of Computer Science and Information Technology     Open Access  
Asian Journal of Control     Hybrid Journal  
Assembly Automation     Hybrid Journal   (Followers: 2)
at - Automatisierungstechnik     Hybrid Journal   (Followers: 1)
Australian Educational Computing     Open Access   (Followers: 1)
Automatic Control and Computer Sciences     Hybrid Journal   (Followers: 4)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Automatica     Hybrid Journal   (Followers: 11)
Automation in Construction     Hybrid Journal   (Followers: 6)
Autonomous Mental Development, IEEE Transactions on     Hybrid Journal   (Followers: 9)
Basin Research     Hybrid Journal   (Followers: 5)
Behaviour & Information Technology     Hybrid Journal   (Followers: 52)
Biodiversity Information Science and Standards     Open Access  
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Biomedical Engineering and Computational Biology     Open Access   (Followers: 14)
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Briefings in Bioinformatics     Hybrid Journal   (Followers: 47)
British Journal of Educational Technology     Hybrid Journal   (Followers: 137)
Broadcasting, IEEE Transactions on     Hybrid Journal   (Followers: 10)
c't Magazin fuer Computertechnik     Full-text available via subscription   (Followers: 2)
CALCOLO     Hybrid Journal  
Calphad     Hybrid Journal  
Canadian Journal of Electrical and Computer Engineering     Full-text available via subscription   (Followers: 14)
Capturing Intelligence     Full-text available via subscription  
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal   (Followers: 2)
Cell Communication and Signaling     Open Access   (Followers: 2)
Central European Journal of Computer Science     Hybrid Journal   (Followers: 5)
CERN IdeaSquare Journal of Experimental Innovation     Open Access   (Followers: 1)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
Chemometrics and Intelligent Laboratory Systems     Hybrid Journal   (Followers: 14)
ChemSusChem     Hybrid Journal   (Followers: 7)
China Communications     Full-text available via subscription   (Followers: 7)
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 2)
CIN Computers Informatics Nursing     Full-text available via subscription   (Followers: 11)
Circuits and Systems     Open Access   (Followers: 15)
Clean Air Journal     Full-text available via subscription   (Followers: 2)
CLEI Electronic Journal     Open Access  
Clin-Alert     Hybrid Journal   (Followers: 1)
Cluster Computing     Hybrid Journal   (Followers: 1)
Cognitive Computation     Hybrid Journal   (Followers: 4)
COMBINATORICA     Hybrid Journal  
Combustion Theory and Modelling     Hybrid Journal   (Followers: 14)
Communication Methods and Measures     Hybrid Journal   (Followers: 12)
Communication Theory     Hybrid Journal   (Followers: 20)
Communications Engineer     Hybrid Journal   (Followers: 1)
Communications in Algebra     Hybrid Journal   (Followers: 3)
Communications in Partial Differential Equations     Hybrid Journal   (Followers: 3)
Communications of the ACM     Full-text available via subscription   (Followers: 55)
Communications of the Association for Information Systems     Open Access   (Followers: 18)
COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering     Hybrid Journal   (Followers: 3)
Complex & Intelligent Systems     Open Access   (Followers: 1)
Complex Adaptive Systems Modeling     Open Access  
Complex Analysis and Operator Theory     Hybrid Journal   (Followers: 2)
Complexity     Hybrid Journal   (Followers: 6)
Complexus     Full-text available via subscription  
Composite Materials Series     Full-text available via subscription   (Followers: 9)
Computación y Sistemas     Open Access  
Computation     Open Access  
Computational and Applied Mathematics     Hybrid Journal   (Followers: 2)
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 2)
Computational and Structural Biotechnology Journal     Open Access   (Followers: 2)
Computational and Theoretical Chemistry     Hybrid Journal   (Followers: 9)
Computational Astrophysics and Cosmology     Open Access   (Followers: 1)
Computational Biology and Chemistry     Hybrid Journal   (Followers: 11)
Computational Chemistry     Open Access   (Followers: 2)
Computational Cognitive Science     Open Access   (Followers: 2)
Computational Complexity     Hybrid Journal   (Followers: 4)
Computational Condensed Matter     Open Access  
Computational Ecology and Software     Open Access   (Followers: 9)
Computational Economics     Hybrid Journal   (Followers: 9)
Computational Geosciences     Hybrid Journal   (Followers: 15)
Computational Linguistics     Open Access   (Followers: 22)
Computational Management Science     Hybrid Journal  
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 4)
Computational Methods and Function Theory     Hybrid Journal  
Computational Molecular Bioscience     Open Access   (Followers: 2)
Computational Optimization and Applications     Hybrid Journal   (Followers: 7)
Computational Particle Mechanics     Hybrid Journal   (Followers: 1)
Computational Research     Open Access   (Followers: 1)
Computational Science and Discovery     Full-text available via subscription   (Followers: 2)
Computational Science and Techniques     Open Access  
Computational Statistics     Hybrid Journal   (Followers: 14)
Computational Statistics & Data Analysis     Hybrid Journal   (Followers: 30)
Computer     Full-text available via subscription   (Followers: 91)
Computer Aided Surgery     Hybrid Journal   (Followers: 5)
Computer Applications in Engineering Education     Hybrid Journal   (Followers: 8)
Computer Communications     Hybrid Journal   (Followers: 10)
Computer Engineering and Applications Journal     Open Access   (Followers: 5)
Computer Journal     Hybrid Journal   (Followers: 9)
Computer Methods in Applied Mechanics and Engineering     Hybrid Journal   (Followers: 22)
Computer Methods in Biomechanics and Biomedical Engineering     Hybrid Journal   (Followers: 12)
Computer Methods in the Geosciences     Full-text available via subscription   (Followers: 2)
Computer Music Journal     Hybrid Journal   (Followers: 18)
Computer Physics Communications     Hybrid Journal   (Followers: 6)
Computer Science - Research and Development     Hybrid Journal   (Followers: 8)
Computer Science and Engineering     Open Access   (Followers: 19)
Computer Science and Information Technology     Open Access   (Followers: 13)
Computer Science Education     Hybrid Journal   (Followers: 14)
Computer Science Journal     Open Access   (Followers: 22)

        1 2 3 4 5 6 | Last

Journal Cover Applied Numerical Mathematics
  [SJR: 1.254]   [H-I: 56]   [5 followers]  Follow
   Hybrid Journal Hybrid journal (It can contain Open Access articles)
   ISSN (Print) 0168-9274 - ISSN (Online) 0168-9274
   Published by Elsevier Homepage  [3123 journals]
  • l2 superconvergence analysis of nonconforming element approximation for 3D
           time-harmonic Maxwell's equations
    • Abstract: Publication date: May 2018
      Source:Applied Numerical Mathematics, Volume 127
      Author(s): Peizhen Wang, Ming Sun, Changhui Yao
      In this paper, the superconvergent property is found for the interpolation error of the nonconforming finite element at element centers. Based upon this property, the superconvergence results in the discrete l 2 norm for the solutions E → , H → and c u r l → E → are presented for the 3D time-harmonic Maxwell's equations. In order to get the global superconvergence, a new postprocess operator derived from the rotated Q 1 element interpolation is constructed, which is based on the superconvergence points. All theoretical results are justified by the provided smoothing and non-smoothing numerical tests.

      PubDate: 2018-01-10T12:44:33Z
  • Two methods based on bivariate spline quasi-interpolants for solving
           Fredholm integral equations
    • Abstract: Publication date: May 2018
      Source:Applied Numerical Mathematics, Volume 127
      Author(s): D. Barrera, F. Elmokhtari, D. Sbibih
      For solving a Fredholm integral equation of the second kind, we approximate its kernel by two types of bivariate spline quasi-interpolants, namely the tensor product and the continuous blending sum of univariate spline quasi-interpolants. We give the construction of the approximate solutions, and we prove some theoretical results related to the approximation errors of these methods. We illustrate the obtained results by some numerical tests giving a comparison with several methods in the literature.

      PubDate: 2018-01-10T12:44:33Z
  • Efficient general linear methods for a class of Volterra
           integro-differential equations
    • Abstract: Publication date: May 2018
      Source:Applied Numerical Mathematics, Volume 127
      Author(s): H. Mahdi, A. Abdi, G. Hojjati
      This paper concerns on the introduction of a method for solving a class of Volterra integro-differential equations (VIDEs) of the second kind. It is based on the combination of special general linear methods for ordinary differential equations and Gregory quadrature rule and equipped with a starting procedure. The convergence and stability of the method are analyzed. Some numerical experiments are given to illustrate the agreement of our implementation with the theoretical convergence orders and show the capability of the method in solving nonlinear VIDEs.

      PubDate: 2018-01-10T12:44:33Z
  • Quasi-Monte Carlo integration on manifolds with mapped low-discrepancy
           points and greedy minimal Riesz s-energy points
    • Abstract: Publication date: May 2018
      Source:Applied Numerical Mathematics, Volume 127
      Author(s): Stefano De Marchi, Giacomo Elefante
      In this paper we consider two sets of points for Quasi-Monte Carlo integration on two-dimensional manifolds. The first is the set of mapped low-discrepancy sequence by a measure preserving map, from a rectangle U ⊂ R 2 to the manifold. The second is the greedy minimal Riesz s-energy points extracted from a suitable discretization of the manifold. Thanks to the Poppy-seed Bagel Theorem we know that the classes of points with minimal Riesz s-energy, under suitable assumptions, are asymptotically uniformly distributed with respect to the normalized Hausdorff measure. They can then be considered as quadrature points on manifolds via the Quasi-Monte Carlo (QMC) method. On the other hand, we do not know if the greedy minimal Riesz s-energy points are a good choice to integrate functions with the QMC method on manifolds. Through theoretical considerations, by showing some properties of these points and by numerical experiments, we attempt to answer to these questions.

      PubDate: 2018-01-10T12:44:33Z
  • A reduced proper orthogonal decomposition (POD) element free Galerkin
           (POD-EFG) method to simulate two-dimensional solute transport problems and
           error estimate
    • Abstract: Publication date: April 2018
      Source:Applied Numerical Mathematics, Volume 126
      Author(s): Mehdi Dehghan, Mostafa Abbaszadeh
      One meshless method based on the variational weak form is the element free Galerkin method. The element free Galerkin (EFG) method is similar to the finite element method but the test and trial functions for the EFG method are chosen from moving least squares (MLS) approximations. The shape functions of MLS approximation don't have the δ-Kronecker property thus the essential boundary conditions (Dirichlet boundary conditions) can not be applied, directly. On the other hand, there are some shape functions that have the mentioned property. One of these functions is the radial point interpolation method (RPIM). In the current paper, we employ the shape functions of RPIM as the test and trial functions. We apply the EFG method based on the RPIM (EFG-RPIM) for solving two-dimensional solute transport problems. To reduce the used CPU time, the proper orthogonal decomposition (POD) approach has been combined with the EFG-RPIM technique. Also, the unconditional stability and convergence of POD-EFG-RPIM method are proved by the energy method. Finally, some numerical results have been reported to show the efficiency and computational order of the new method.

      PubDate: 2018-01-10T12:44:33Z
  • Corrigendum to “The matrix splitting based proximal fixed-point
           algorithms for quadratically constrained ℓ1 minimization and Dantzig
           selector” [Appl. Numer. Math. 125 (2018) 23–50]
    • Abstract: Publication date: April 2018
      Source:Applied Numerical Mathematics, Volume 126
      Author(s): Yongchao Yu, Jigen Peng

      PubDate: 2018-01-10T12:44:33Z
  • Optimal Schwarz waveform relaxation for fractional diffusion-wave
    • Abstract: Publication date: Available online 10 January 2018
      Source:Applied Numerical Mathematics
      Author(s): Giovanna Califano, Dajana Conte
      We introduce domain decomposition methods of Schwarz waveform relaxation (WR) type for fractional diffusion-wave equations. We show that the Dirichlet transmission conditions among the subdomains lead to slow convergence. So, we construct optimal transmission conditions at the artificial interfaces and we prove that optimal Schwarz WR methods on N subdomains converge in N iterations both on infinite spatial domains and on finite spatial domains. We also propose optimal transmission conditions when the original problem is spatially discretized and we prove the same result found in the continuous case.

      PubDate: 2018-01-10T12:44:33Z
  • An a posteriori error estimator for a LPS method for Navier–Stokes
    • Abstract: Publication date: Available online 4 January 2018
      Source:Applied Numerical Mathematics
      Author(s): Rodolfo Araya, Ramiro Rebolledo
      In this work we develop an a posteriori error estimator, of the hierarchical type, for the Local Projection Stabilized (LPS) finite element method introduced in [5], applied to the incompressible Navier–Stokes equations. The technique use the solution of locals problems posed on appropriate finite dimensional spaces of bubble-like functions, to approach the error. Several numerical tests confirm the theoretical properties of the estimator and its performance.

      PubDate: 2018-01-10T12:44:33Z
  • Computing eigenvalues and eigenfunctions of the Laplacian for convex
    • Authors: Matthew J. Colbrook; Athanasisos S. Fokas
      Pages: 1 - 17
      Abstract: Publication date: April 2018
      Source:Applied Numerical Mathematics, Volume 126
      Author(s): Matthew J. Colbrook, Athanasisos S. Fokas
      Recently a new transform method, called the Unified Transform or the Fokas method, for solving boundary value problems (BVPs) for linear and integrable nonlinear partial differential equations (PDEs) has received a lot of attention. For linear elliptic PDEs, this method yields two equations, known as the global relations, coupling the Dirichlet and Neumann boundary values. These equations can be used in a collocation method to determine the Dirichlet to Neumann map. This involves expanding the unknown functions in terms of a suitable basis, and choosing a set of collocation points at which to evaluate the global relations. Here, using these methods for the Helmholtz and modified Helmholtz equations and following the earlier results of [15], we determine eigenvalues of the Laplacian in a convex polygon. Eigenvalues are characterised by the points where the generalised Dirichlet to Neumann map becomes singular. We find that the method yields spectral convergence for eigenfunctions smooth on the boundary and for non-smooth boundary values, the rate of convergence is determined by the rate of convergence of expansions in the chosen Legendre basis. Extensions to the case of oblique derivative boundary conditions and constant coefficient elliptic PDEs are also discussed and demonstrated.

      PubDate: 2017-12-27T08:27:00Z
      DOI: 10.1016/j.apnum.2017.12.001
      Issue No: Vol. 126 (2017)
  • Efficient approaches for enclosing the united solution set of the interval
           generalized Sylvester matrix equations
    • Authors: Marzieh Dehghani-Madiseh; Milan Hladík
      Pages: 18 - 33
      Abstract: Publication date: April 2018
      Source:Applied Numerical Mathematics, Volume 126
      Author(s): Marzieh Dehghani-Madiseh, Milan Hladík
      We investigate the interval generalized Sylvester matrix equation A X B + C X D = F . We propose a necessary condition for its solutions, and also a sufficient condition for boundedness of the whole solution set. The main effort is performed to develop techniques for computing outer estimations of the so-called united solution set of this interval system. First, we propose a modified variant of the Krawczyk operator, reducing significantly computational complexity, compared to the Kronecker product form. We then propose an iterative technique for enclosing the solution set. These approaches are based on spectral decompositions of the midpoints of A, B, C and D and in both of them we suppose that the midpoints of A and C are simultaneously diagonalizable as well as for the midpoints of the matrices B and D. Numerical experiments are given to illustrate the performance of the proposed methods.

      PubDate: 2017-12-27T08:27:00Z
      DOI: 10.1016/j.apnum.2017.12.003
      Issue No: Vol. 126 (2017)
  • An explicit spectral collocation method for the linearized Korteweg–de
           Vries equation on unbounded domain
    • Authors: Jinwei Fang; Boying Wu; Wenjie Liu
      Pages: 34 - 52
      Abstract: Publication date: April 2018
      Source:Applied Numerical Mathematics, Volume 126
      Author(s): Jinwei Fang, Boying Wu, Wenjie Liu
      In this paper, we present a stable and efficient numerical scheme for the linearized Korteweg–de Vries equation on unbounded domain. After employing the Crank–Nicolson method for temporal discretization, the transparent boundary conditions are derived for the time semi-discrete scheme. Then the unconditional stability of the resulting initial boundary problem is established. For spatial discretization, we construct a non-polynomial based spectral collocation method in which the basis functions are built upon a generalized Birkhoff interpolation. The interpolation error of the new basis is also investigated. Moreover, the basis functions build in two free parameters intrinsically which can be chosen properly so that the implicit time semi-discrete scheme collapses to an explicit scheme after spatial discretization. Numerical tests are performed to demonstrate the stability and accuracy of the proposed method.

      PubDate: 2017-12-27T08:27:00Z
      DOI: 10.1016/j.apnum.2017.11.008
      Issue No: Vol. 126 (2017)
  • Analysis of a dynamic contact problem with nonmonotone friction and
           non-clamped boundary conditions
    • Authors: Mikael Barboteu; Krzysztof Bartosz; David Danan
      Pages: 53 - 77
      Abstract: Publication date: April 2018
      Source:Applied Numerical Mathematics, Volume 126
      Author(s): Mikael Barboteu, Krzysztof Bartosz, David Danan
      We consider a dynamic process of frictional contact between a non-clamped viscoelastic body and a foundation. We assume that the normal contact response depends on the depth of penetration of the foundation by the considered body, and the dependence between these two quantities is governed by normal compliance conditions. On the other hand, the friction force is assumed to be a nonmonotone function of the slip rate where the friction threshold also depends on the depth of the penetration. Our aim in this paper is twofold. The first one is to prove the existence and the uniqueness of a weak solution for the contact problem under consideration. The second one is to provide the numerical analysis of the process involving its semi-discrete and fully discrete approximation as well as estimation of the error for both numerical schemes and the validation of such a result.

      PubDate: 2017-12-27T08:27:00Z
      DOI: 10.1016/j.apnum.2017.12.005
      Issue No: Vol. 126 (2017)
  • Increasing the approximation order of the triangular Shepard method
    • Authors: F. Dell'Accio; F. Di Tommaso; O. Nouisser; B. Zerroudi
      Pages: 78 - 91
      Abstract: Publication date: April 2018
      Source:Applied Numerical Mathematics, Volume 126
      Author(s): F. Dell'Accio, F. Di Tommaso, O. Nouisser, B. Zerroudi
      In this paper we discuss an improvement of the triangular Shepard operator proposed by Little to extend the Shepard method. In particular, we use triangle based basis functions in combination with a modified version of the linear local interpolant on the vertices of the triangle. We deeply study the resulting operator, which uses functional and derivative data, has cubic approximation order and a good accuracy of approximation. Suggestions on how to avoid the use of derivative data, without losing both order and accuracy of approximation, are given.

      PubDate: 2017-12-27T08:27:00Z
      DOI: 10.1016/j.apnum.2017.12.006
      Issue No: Vol. 126 (2017)
  • Parameter selection for HOTV regularization
    • Authors: Toby Sanders
      Pages: 1 - 9
      Abstract: Publication date: March 2018
      Source:Applied Numerical Mathematics, Volume 125
      Author(s): Toby Sanders
      Popular methods for finding regularized solutions to inverse problems include sparsity promoting ℓ 1 regularization techniques, one in particular which is the well known total variation (TV) regularization. More recently, several higher order (HO) methods similar to TV have been proposed, which we generally refer to as HOTV methods. In this letter, we investigate the problem of the often debated selection of λ, the parameter used to carefully balance the interplay between data fitting and regularization terms. We theoretically argue for a scaling of the operators for a uniform parameter selection for all orders of HOTV regularization. In particular, parameter selection for all orders of HOTV may be determined by scaling an initial parameter for TV, which the imaging community may be more familiar with. We also provide several numerical results which justify our theoretical findings.

      PubDate: 2017-11-09T09:57:16Z
      DOI: 10.1016/j.apnum.2017.10.010
      Issue No: Vol. 125 (2017)
  • A pseudospectral scheme and its convergence analysis for high-order
           integro-differential equations
    • Authors: Xiaojun Tang; Heyong Xu
      Pages: 51 - 67
      Abstract: Publication date: March 2018
      Source:Applied Numerical Mathematics, Volume 125
      Author(s): Xiaojun Tang, Heyong Xu
      The main purpose of this work is to develop an integral pseudospectral scheme for solving integro-differential equations. We provide new pseudospectral integration matrices (PIMs) for the Legendre–Gauss and the flipped Legendre–Gauss–Radau points, respectively, and present an efficient and stable approach to computing the PIMs via the recursive calculation of Legendre integration matrices. Furthermore, we provide a rigorous convergence analysis for the proposed pseudospectral scheme in both L ∞ and L 2 spaces via a linear integral equation, and the spectral rate of convergence is demonstrated by numerical results.

      PubDate: 2017-11-16T11:59:56Z
      DOI: 10.1016/j.apnum.2017.10.003
      Issue No: Vol. 125 (2017)
  • Fast computation of stationary joint probability distribution of sparse
           Markov chains
    • Authors: Weiyang Ding; Michael Ng; Yimin Wei
      Pages: 68 - 85
      Abstract: Publication date: March 2018
      Source:Applied Numerical Mathematics, Volume 125
      Author(s): Weiyang Ding, Michael Ng, Yimin Wei
      In this paper, we study a fast algorithm for finding stationary joint probability distributions of sparse Markov chains or multilinear PageRank vectors which arise from data mining applications. In these applications, the main computational problem is to calculate and store solutions of many unknowns in joint probability distributions of sparse Markov chains. Our idea is to approximate large-scale solutions of such sparse Markov chains by two components: the sparsity component and the rank-one component. Here the non-zero locations in the sparsity component refer to important associations in the joint probability distribution and the rank-one component refers to a background value of the solution. We propose to determine solutions by formulating and solving sparse and rank-one optimization problems via closed form solutions. The convergence of the truncated power method is established. Numerical examples of multilinear PageRank vector calculation and second-order web-linkage analysis are presented to show the efficiency of the proposed method. It is shown that both computation and storage are significantly reduced by comparing with the traditional power method.

      PubDate: 2017-11-16T11:59:56Z
      DOI: 10.1016/j.apnum.2017.10.008
      Issue No: Vol. 125 (2017)
  • Quadratic/linear rational spline collocation for linear boundary value
    • Authors: Erge Ideon; Peeter Oja
      Pages: 143 - 158
      Abstract: Publication date: March 2018
      Source:Applied Numerical Mathematics, Volume 125
      Author(s): Erge Ideon, Peeter Oja
      We investigate the collocation method with quadratic/linear rational spline S of smoothness class C 2 for the numerical solution of two-point boundary value problems if the solution y (or −y) of the boundary value problem is a strictly convex function. We show that on the uniform mesh it holds ‖ S − y ‖ ∞ = O ( h 2 ) . Established bound of error gives a dependence on the solution of the boundary value problem and its coefficient functions. We prove also convergence rates ‖ S ′ − y ′ ‖ ∞ = O ( h 2 ) and ‖ S ″ − y ″ ‖ ∞ = O ( h 2 ) . Numerical examples support the obtained theoretical results.

      PubDate: 2017-12-27T08:27:00Z
      DOI: 10.1016/j.apnum.2017.11.005
      Issue No: Vol. 125 (2017)
  • The second order perturbation approach for elliptic partial differential
           equations on random domains
    • Authors: Helmut Harbrecht; Michael D. Peters
      Pages: 159 - 171
      Abstract: Publication date: March 2018
      Source:Applied Numerical Mathematics, Volume 125
      Author(s): Helmut Harbrecht, Michael D. Peters
      The present article is dedicated to the solution of elliptic boundary value problems on random domains. We apply a high-precision second order shape Taylor expansion to quantify the impact of the random perturbation on the solution. Thus, we obtain a representation of the solution with third order accuracy in the size of the perturbation's amplitude. The major advantage of this approach is that we end up with purely deterministic equations for the solution's moments. In particular, we derive representations for the first four moments, i.e., expectation, variance, skewness and kurtosis. These moments are efficiently computable by means of boundary integral equations. Numerical results are presented to validate the presented approach.

      PubDate: 2017-12-27T08:27:00Z
      DOI: 10.1016/j.apnum.2017.11.002
      Issue No: Vol. 125 (2017)
  • A discrete divergence free weak Galerkin finite element method for the
           Stokes equations
    • Authors: Lin Mu; Junping Wang; Xiu Ye; Shangyou Zhang
      Pages: 172 - 182
      Abstract: Publication date: March 2018
      Source:Applied Numerical Mathematics, Volume 125
      Author(s): Lin Mu, Junping Wang, Xiu Ye, Shangyou Zhang
      A discrete divergence free weak Galerkin finite element method is developed for the Stokes equations based on a weak Galerkin (WG) method introduced in [17]. Discrete divergence free bases are constructed explicitly for the lowest order weak Galerkin elements in two and three dimensional spaces. These basis functions can be derived on general meshes of arbitrary shape of polygons and polyhedrons. With the divergence free basis derived, the discrete divergence free WG scheme can eliminate pressure variable from the system and reduces a saddle point problem to a symmetric and positive definite system with many fewer unknowns. Numerical results are presented to demonstrate the robustness and accuracy of this discrete divergence free WG method.

      PubDate: 2017-12-27T08:27:00Z
      DOI: 10.1016/j.apnum.2017.11.006
      Issue No: Vol. 125 (2017)
  • Conforming finite element methods for the stochastic
           Cahn–Hilliard–Cook equation
    • Authors: Shimin Chai; Yanzhao Cao; Yongkui Zou; Wenju Zhao
      Pages: 44 - 56
      Abstract: Publication date: February 2018
      Source:Applied Numerical Mathematics, Volume 124
      Author(s): Shimin Chai, Yanzhao Cao, Yongkui Zou, Wenju Zhao
      This paper is concerned with the finite element approximation of the stochastic Cahn–Hilliard–Cook equation driven by an infinite dimensional Wiener type noise. The Argyris finite elements are used to discretize the spatial variables while the infinite dimensional (cylindrical) Wiener process is approximated by truncated stochastic series spanned by the spectral basis of the covariance operator. The optimal strong convergence order in L 2 and H ˙ − 2 norms is obtained. Unlike the mixed finite element method studied in the existing literature, our method allows the covariance operator of the Wiener process to have an infinite trace, including the space–time white noise is allowed in our model. Numerical experiments are presented to illustrate the theoretical analysis.

      PubDate: 2017-10-25T12:06:02Z
      DOI: 10.1016/j.apnum.2017.09.010
      Issue No: Vol. 124 (2017)
  • A high-order fully conservative block-centered finite difference method
           for the time-fractional advection–dispersion equation
    • Authors: Xiaoli Li; Hongxing Rui
      Pages: 89 - 109
      Abstract: Publication date: February 2018
      Source:Applied Numerical Mathematics, Volume 124
      Author(s): Xiaoli Li, Hongxing Rui
      Based on the weighted and shifted Grünwald–Letnikov difference operator, a new high-order block-centered finite difference method is derived for the time-fractional advection–dispersion equation by introducing an auxiliary flux variable to guarantee full mass conservation. The stability and the global convergence of the scheme are proved rigorously. Some a priori estimates of discrete norms with optimal order of convergence O ( Δ t 3 + h 2 + k 2 ) both for solute concentration and the auxiliary flux variable are established on non-uniform rectangular grids, where Δ t ,   h and k are the step sizes in time, space in x- and y-direction. Moreover, the applicability and accuracy of the scheme are demonstrated by numerical experiments to support our theoretical analysis.

      PubDate: 2017-11-02T09:17:53Z
      DOI: 10.1016/j.apnum.2017.10.004
      Issue No: Vol. 124 (2017)
  • The fictitious domain method with H1-penalty for the Stokes problem with
           Dirichlet boundary condition
    • Authors: Guanyu Zhou
      Pages: 1 - 21
      Abstract: Publication date: January 2018
      Source:Applied Numerical Mathematics, Volume 123
      Author(s): Guanyu Zhou
      We consider the fictitious domain method with H 1 -penalty for the Stokes problem with Dirichlet boundary condition. First, for the continuous penalty problem, we obtain the optimal error estimate O ( ϵ ) for both the velocity and pressure, where ϵ is the penalty parameter. Moreover, we investigate the H m -regularity for the solution of the penalty problem. Then, we apply the finite element method with the P1/P1 element to the penalty problem. Since the solution to the penalty problem has a jump in the traction vector, we introduce some interpolation/projection operators, as well as an inf-sup condition with the norm depending on ϵ. With the help of these preliminaries, we derive the error estimates for the finite element approximation. The theoretical results are verified by the numerical experiments.

      PubDate: 2017-09-26T13:37:25Z
      DOI: 10.1016/j.apnum.2017.08.005
      Issue No: Vol. 123 (2017)
  • Implicit–Explicit WENO scheme for the equilibrium dispersive model
           of chromatography
    • Authors: R. Donat; F. Guerrero; P. Mulet
      Pages: 22 - 42
      Abstract: Publication date: January 2018
      Source:Applied Numerical Mathematics, Volume 123
      Author(s): R. Donat, F. Guerrero, P. Mulet
      Chromatographic processes can be modeled by nonlinear, convection-dominated partial differential equations, together with nonlinear relations: the adsorption isotherms. In this paper we consider the nonlinear equilibrium dispersive (ED) model with adsorption isotherms of Langmuir type. We show that, in this case, the ED model can be written as a system of conservation laws when the dispersion coefficient vanishes. We also show that the function that relates the conserved variables and the physically observed concentrations of the components in the mixture is one to one and it admits a global inverse, which cannot be given explicitly, but can be adequately computed. As a result, fully conservative numerical schemes can be designed for the ED model in chromatography. We propose a Weighted-Essentially-non-Oscillatory second order IMEX scheme and describe the numerical issues involved in its application. Through a series of numerical experiments, we show that our scheme gives accurate numerical solutions which capture the sharp discontinuities present in the chromatographic fronts, with the same stability restrictions as in the purely hyperbolic case.

      PubDate: 2017-09-26T13:37:25Z
      DOI: 10.1016/j.apnum.2017.08.008
      Issue No: Vol. 123 (2017)
  • Fractional PDE constrained optimization: An optimize-then-discretize
           approach with L-BFGS and approximate inverse preconditioning
    • Authors: Stefano Cipolla; Fabio Durastante
      Pages: 43 - 57
      Abstract: Publication date: January 2018
      Source:Applied Numerical Mathematics, Volume 123
      Author(s): Stefano Cipolla, Fabio Durastante
      In this paper, using an optimize-then-discretize approach, we address the numerical solution of two Fraction Partial Differential Equation constrained optimization problems: the Fractional Advection Dispersion Equation (FADE) and the two-dimensional semilinear Riesz Space Fractional Diffusion equation. Both a theoretical and experimental analysis of the problem is carried out. The algorithmic framework is based on the L-BFGS method coupled with a Krylov subspace solver. A suitable preconditioning strategy by approximate inverses is taken into account. Graphics Processing Unit (GPU) accelerator is used in the construction of the preconditioners. The numerical experiments are performed with benchmarked software/libraries enforcing the reproducibility of the results.

      PubDate: 2017-09-26T13:37:25Z
      DOI: 10.1016/j.apnum.2017.09.001
      Issue No: Vol. 123 (2017)
  • Algorithms for the implementation of adaptive isogeometric methods using
           hierarchical B-splines
    • Authors: Eduardo M. Garau; Rafael Vázquez
      Pages: 58 - 87
      Abstract: Publication date: January 2018
      Source:Applied Numerical Mathematics, Volume 123
      Author(s): Eduardo M. Garau, Rafael Vázquez
      In this article we introduce all the ingredients to develop adaptive isogeometric methods based on hierarchical B-splines. In particular, we give precise definitions of local refinement and coarsening that, unlike previously existing methods, can be understood as the inverse of each other. We also define simple and intuitive data structures for the implementation of hierarchical B-splines, and algorithms for refinement and coarsening that take advantage of local information. We complete the paper with some simple numerical tests to show the performance of the data structures and algorithms, that have been implemented in the open-source Octave/Matlab code GeoPDEs.

      PubDate: 2017-09-26T13:37:25Z
      DOI: 10.1016/j.apnum.2017.08.006
      Issue No: Vol. 123 (2017)
  • Supercloseness of the continuous interior penalty method for singularly
           perturbed problems in 1D: Vertex-cell interpolation
    • Authors: Jin Zhang; Xiaowei Liu
      Pages: 88 - 98
      Abstract: Publication date: January 2018
      Source:Applied Numerical Mathematics, Volume 123
      Author(s): Jin Zhang, Xiaowei Liu
      A continuous interior penalty method with piecewise polynomials of degree p ≥ 2 is applied on a Shishkin mesh to solve a singularly perturbed convection–diffusion problem, whose solution has a single boundary layer. This method is analyzed by means of a series of integral identities developed for the convection terms. Then we prove a supercloseness bound of order 5/2 for a vertex-cell interpolation when p = 2 . The sharpness of our analysis is supported by some numerical experiments. Moreover, numerical tests show supercloseness clearly for p ≥ 3 .

      PubDate: 2017-09-26T13:37:25Z
      DOI: 10.1016/j.apnum.2017.09.003
      Issue No: Vol. 123 (2017)
  • Fully spectral collocation method for nonlinear parabolic partial
           integro-differential equations
    • Authors: Farhad Fakhar-Izadi; Mehdi Dehghan
      Pages: 99 - 120
      Abstract: Publication date: January 2018
      Source:Applied Numerical Mathematics, Volume 123
      Author(s): Farhad Fakhar-Izadi, Mehdi Dehghan
      The numerical approximation of solution to nonlinear parabolic Volterra and Fredholm partial integro-differential equations is studied in this paper. Unlike the conventional methods which discretize the time variable by finite difference schemes, we use the spectral method for this purpose. Indeed, both of the space and time discretizations are based on the Legendre-collocation method which lead to conversion of the problem to a nonlinear system of algebraic equations. The convergence of the proposed method is proven by providing an L ∞ error estimate. Several numerical examples are included to demonstrate the efficiency and spectral accuracy of the proposed method in the space and time directions.

      PubDate: 2017-10-03T14:25:01Z
      DOI: 10.1016/j.apnum.2017.08.007
      Issue No: Vol. 123 (2017)
  • Solving a class of nonlinear boundary integral equations based on the
           meshless local discrete Galerkin (MLDG) method
    • Authors: Pouria Assari; Mehdi Dehghan
      Pages: 137 - 158
      Abstract: Publication date: January 2018
      Source:Applied Numerical Mathematics, Volume 123
      Author(s): Pouria Assari, Mehdi Dehghan
      The main purpose of this article is to investigate a computational scheme for solving a class of nonlinear boundary integral equations which occurs as a reformulation of boundary value problems of Laplace's equations with nonlinear Robin boundary conditions. The method approximates the solution by the Galerkin method based on the use of moving least squares (MLS) approach as a locally weighted least square polynomial fitting. The discrete Galerkin method for solving boundary integral equations results from the numerical integration of all integrals appeared in the method. The numerical scheme developed in the current paper utilizes the non-uniform Gauss–Legendre quadrature rule to estimate logarithm-like singular integrals. Since the proposed method is constructed on a set of scattered points, it does not require any background mesh and so we can call it as the meshless local discrete Galerkin (MLDG) method. The scheme is simple and effective to solve boundary integral equations and its algorithm can be easily implemented. We also obtain the error bound and the convergence rate of the presented method. Finally, numerical examples are included to show the validity and efficiency of the new technique and confirm the theoretical error estimates.

      PubDate: 2017-10-03T14:25:01Z
      DOI: 10.1016/j.apnum.2017.09.002
      Issue No: Vol. 123 (2017)
  • Line integral solution of Hamiltonian systems with holonomic constraints
    • Authors: Luigi Brugnano; Gianmarco Gurioli; Felice Iavernaro; Ewa B. Weinmüller
      Abstract: Publication date: Available online 24 December 2017
      Source:Applied Numerical Mathematics
      Author(s): Luigi Brugnano, Gianmarco Gurioli, Felice Iavernaro, Ewa B. Weinmüller
      In this paper, we propose a second-order energy-conserving approximation procedure for Hamiltonian systems with holonomic constraints. The derivation of the procedure relies on the use of the so-called line integral framework. We provide numerical experiments to illustrate theoretical findings.

      PubDate: 2017-12-27T08:27:00Z
      DOI: 10.1016/j.apnum.2017.12.014
  • Criteria for hexahedral cell classification
    • Authors: Olga V. Ushakova
      Abstract: Publication date: Available online 20 December 2017
      Source:Applied Numerical Mathematics
      Author(s): Olga V. Ushakova
      The aim of the paper is to give the numerical criteria for classification of different types of hexahedral cells which can emerge in a three-dimensional structured grid generation. In general, computational grids and their cells have to be nondegenerate, however, in practice, situations arise in which degenerate grids are used and computed. In these cases, to prevent lost of accuracy, special strategies must be chosen both in grid generation and physical phenomenon solution algorithms. To determine which cells need a modification in above strategies, degenerate cells have to be detected. The criteria are suggested for hexahedral cells constructed by a trilinear mapping of the unit cube. All hexahedral cells are divided into nondegenerate and degenerate. Among nondegenerate hexahedral cells, cells exotic in shape are singled out as inadmissible. Degenerate cells are divided into pyramids, prisms and tetrahedrons—types of cells which can be admissible in grid generation and solution algorithms. Inadmissible types of degenerations are also considered. An algorithm for testing three-dimensional structured grids according to suggested criteria is described. Both results of testing and examples of different types of cells are demonstrated. In conclusion, recommendations for structured grid generation with the purpose to exclude undesirable types of cells are given.

      PubDate: 2017-12-27T08:27:00Z
      DOI: 10.1016/j.apnum.2017.12.012
  • A conforming enriched finite element method for elliptic interface
    • Authors: Hua Wang; Jinru Chen; Pengtao Sun; Fangfang Qin
      Abstract: Publication date: Available online 20 December 2017
      Source:Applied Numerical Mathematics
      Author(s): Hua Wang, Jinru Chen, Pengtao Sun, Fangfang Qin
      A new conforming enriched finite element method is presented for elliptic interface problems with interface-unfitted meshes. The conforming enriched finite element space is constructed based on the P 1 -conforming finite element space. Approximation capability of the conforming enriched finite element space is analyzed. The standard conforming Galerkin method is considered without any penalty stabilization term. Our method does not limit the diffusion coefficient of the elliptic interface problem to a piecewise constant. Finite element errors in H 1 -norm and L 2 -norm are proved to be optimal. Numerical experiments are carried out to validate theoretical results.

      PubDate: 2017-12-27T08:27:00Z
      DOI: 10.1016/j.apnum.2017.12.011
  • Shape optimization for Stokes flows using sensitivity analysis and finite
           element method
    • Authors: V.C. Le; H.T. Pham; T.T.M. Ta
      Abstract: Publication date: Available online 20 December 2017
      Source:Applied Numerical Mathematics
      Author(s): V.C. Le, H.T. Pham, T.T.M. Ta
      In the context of structural optimization in fluid mechanics we propose a numerical method based on a combination of the classical shape derivative and Hadamard's boundary variation method. Our approach regards the viscous flows governed by Stokes equations with the objective function of energy dissipation and a constrained volume. The shape derivative is computed by Lagrange's approach via the solutions of Stokes and adjoint systems. The programs are written in FreeFem++ using the Finite Element method.

      PubDate: 2017-12-27T08:27:00Z
      DOI: 10.1016/j.apnum.2017.12.009
  • Discrete Modified Projection Method for Urysohn Integral Equations with
           Smooth Kernels
    • Authors: Rekha P. Kulkarni; Gobinda Rakshit
      Abstract: Publication date: Available online 18 December 2017
      Source:Applied Numerical Mathematics
      Author(s): Rekha P. Kulkarni, Gobinda Rakshit
      Approximate solutions of linear and nonlinear integral equations using methods related to an interpolatory projection involve many integrals which need to be evaluated using a numerical quadrature formula. In this paper, we consider discrete versions of the modified projection method and of the iterated modified projection method for solution of a Urysohn integral equation with a smooth kernel. For r ≥ 1 , a space of piecewise polynomials of degree ≤ r − 1 with respect to an uniform partition is chosen to be the approximating space and the projection is chosen to be the interpolatory projection at r Gauss points. The orders of convergence which we obtain for these discrete versions indicate the choice of numerical quadrature which preserves the orders of convergence. Numerical results are given for a specific example.

      PubDate: 2017-12-27T08:27:00Z
      DOI: 10.1016/j.apnum.2017.12.008
  • Error analysis of the high order scheme for homogenization of
           Hamilton–Jacobi equation
    • Authors: Xinpeng Yuan; Chunguang Xiong Guoqing Zhu
      Abstract: Publication date: Available online 14 December 2017
      Source:Applied Numerical Mathematics
      Author(s): Xinpeng Yuan, Chunguang Xiong, Guoqing Zhu
      In this paper, employing ideas developed for conservation law equations such as the Lax–Friedrich-type and Godunov-type numerical fluxes, we describe the numerical schemes for approximating the solution of the limit problem arising in the homogenization of Hamilton–Jacobi equations. All approximation methods involve three steps. The first scheme is a provably monotonic discretization of the cell problem for approximating the effective Hamiltonian for a given vector P ∈ R N . Next, using interpolation, we present an approximation of the effective Hamiltonian in the domain R N . Finally, the numerical schemes of the Hamilton–Jacobi equations with the effective Hamiltonian approximation are constructed. We also present global error estimates including all the discrete mesh sizes. The theoretical results are illustrated through numerical examples, including two convex Hamiltonians and two non-convex Hamiltonians.

      PubDate: 2017-12-27T08:27:00Z
  • Mixed recurrence equations and interlacing properties for zeros of
           sequences of classical q-orthogonal polynomials
    • Authors: D.D. Tcheutia; A.S. Jooste; W. Koepf
      Abstract: Publication date: Available online 14 November 2017
      Source:Applied Numerical Mathematics
      Author(s): D.D. Tcheutia, A.S. Jooste, W. Koepf
      Using the q-version of Zeilberger's algorithm, we provide a procedure to find mixed recurrence equations satisfied by classical q-orthogonal polynomials with shifted parameters. These equations are used to investigate interlacing properties of zeros of sequences of q-orthogonal polynomials. In the cases where zeros do not interlace, we give some numerical examples to illustrate this.

      PubDate: 2017-11-16T11:59:56Z
      DOI: 10.1016/j.apnum.2017.11.003
  • The Crank-Nicolson/Adams-Bashforth scheme for the Burgers equation with H2
           and H1 initial data
    • Authors: Tong Zhang; JiaoJiao Jin; YuGao HuangFu
      Abstract: Publication date: Available online 10 November 2017
      Source:Applied Numerical Mathematics
      Author(s): Tong Zhang, JiaoJiao Jin, YuGao HuangFu
      In this paper, we consider the stability and convergence results of the Crank-Nicolson/Adams-Bashforth scheme for the Burgers equation with smooth and nonsmooth initial data. The spatial approximation is based on the standard conforming finite element space. The temporal treatment of the spatial discrete Burgers equation is based on the implicit Crank-Nicolson scheme for the linear term and the explicit Adams-Bashforth scheme for the nonlinear term. Firstly, we prove that the Crank-Nicolson/Adams-Bashforth scheme is almost unconditionally stable with initial data u 0 ∈ H α ( α = 1 , 2 ) . Secondly, the optimal error estimates of the numerical solution in L 2 -norm are derived with initial data u 0 ∈ H 2 , and the error estimates of approximate solution in L 2 norm obtained with initial data u 0 ∈ H 1 is reduced by 1 2 . Finally, some numerical examples are provided to verify the established stability theory and convergence results with H 2 and H 1 initial data.

      PubDate: 2017-11-16T11:59:56Z
      DOI: 10.1016/j.apnum.2017.10.009
  • The matrix splitting based proximal fixed-point algorithms for
           quadratically constrained ℓ1 minimization and Dantzig selector
    • Authors: Yongchao Yu; Jigen Peng
      Abstract: Publication date: Available online 3 November 2017
      Source:Applied Numerical Mathematics
      Author(s): Yongchao Yu, Jigen Peng
      This paper studies algorithms for solving quadratically constrained ℓ 1 minimization and Dantzig selector which have recently been widely used to tackle sparse recovery problems in compressive sensing. The two optimization models can be reformulated via two indicator functions as special cases of a general convex composite model which minimizes the sum of two convex functions with one composed with a matrix operator. The general model can be transformed into a fixed-point problem for a nonlinear operator which is composed of a proximity operator and an expansive matrix operator, and then a new iterative scheme based on the expansive matrix splitting is proposed to find fixed-points of the nonlinear operator. We also give some mild conditions to guarantee that the iterative sequence generated by the scheme converges to a fixed-point of the nonlinear operator. Further, two specific proximal fixed-point algorithms based on the scheme are developed and then applied to quadratically constrained ℓ 1 minimization and Dantzig selector. Numerical results have demonstrated that the proposed algorithms are comparable to the state-of-the-art algorithms for recovering sparse signals with different sizes and dynamic ranges in terms of both accuracy and speed. In addition, we also extend the proposed algorithms to solve two harder constrained total-variation minimization problems.

      PubDate: 2017-11-09T09:57:16Z
      DOI: 10.1016/j.apnum.2017.11.001
  • Splitting schemes for unsteady problems involving the grad-div operator
    • Authors: Peter Minev; Petr N. Vabishchevich
      Abstract: Publication date: Available online 31 October 2017
      Source:Applied Numerical Mathematics
      Author(s): Peter Minev, Petr N. Vabishchevich
      In this paper we consider various splitting schemes for unsteady problems containing the grad-div operator. The fully implicit discretization of such problems would yield at each time step a linear problem that couples all components of the solution vector. In this paper we discuss various possibilities to decouple the equations for the different components that result in unconditionally stable schemes. If the spatial discretization uses Cartesian grids, the resulting schemes are Locally One Dimensional (LOD). The stability analysis of these schemes is based on the general stability theory of additive operator-difference schemes developed by Samarskii and his collaborators. The results of the theoretical analysis are illustrated on a 2D numerical example with a smooth manufactured solution.

      PubDate: 2017-11-02T09:17:53Z
      DOI: 10.1016/j.apnum.2017.10.005
  • Residual error estimation for anisotropic Kirchhoff plates
    • Authors: Michael Weise
      Abstract: Publication date: Available online 31 October 2017
      Source:Applied Numerical Mathematics
      Author(s): Michael Weise
      Residual error estimation for conforming finite element discretisations of the isotropic Kirchhoff plate problem is covered by an estimator of Verfürth for the related biharmonic equation. This article generalises Verfürth's result to Kirchhoff plates with an anisotropic material, which requires some modifications. Special emphasis is laid on the reduced Hsieh–Clough–Tocher triangular finite element, the conforming element with the least possible number of unknowns.

      PubDate: 2017-11-02T09:17:53Z
      DOI: 10.1016/j.apnum.2017.10.007
  • Differential equations for families of semi-classical orthogonal
           polynomials within class one
    • Authors: G. Filipuk; M.N. Rebocho
      Abstract: Publication date: Available online 23 October 2017
      Source:Applied Numerical Mathematics
      Author(s): G. Filipuk, M.N. Rebocho
      In this paper we study families of semi-classical orthogonal polynomials within class one. We derive general second or third order ordinary differential equations (with respect to certain parameters) for the recurrence coefficients of the three-term recurrence relation of these polynomials and show that in particular well-known cases, e.g. related to the modified Airy and Laguerre weights, these equations can be reduced to the second and the fourth Painlevé equations.

      PubDate: 2017-10-25T12:06:02Z
      DOI: 10.1016/j.apnum.2017.10.002
  • A new quadrature scheme based on an Extended Lagrange Interpolation
    • Authors: Donatella Occorsio; Maria Grazia Russo
      Abstract: Publication date: Available online 18 October 2017
      Source:Applied Numerical Mathematics
      Author(s): Donatella Occorsio, Maria Grazia Russo
      Let w ( x ) = e − x β x α , w ¯ ( x ) = x w ( x ) and let { p m ( w ) } m , { p m ( w ¯ ) } m be the corresponding sequences of orthonormal polynomials. Since the zeros of p m + 1 ( w ) interlace those of p m ( w ¯ ) , it makes sense to construct an interpolation process essentially based on the zeros of Q 2 m + 1 : = p m + 1 ( w ) p m ( w ¯ ) , which is called “Extended Lagrange Interpolation". In this paper the convergence of this interpolation process is studied in suitable weighted L 1 spaces, in a general framework which completes the results given by the same authors in weighted L u p ( ( 0 , + ∞ ) ) , 1 ≤ p ≤ ∞ (see [30], [27]). As an application of the theoretical results, an extended product integration rule, based on the aforesaid Lagrange process, is proposed in order to compute integrals of the type ∫ 0 + ∞ f ( x ) k ( x , y ) u ( x ) d x , u ( x ) = e − x β x γ ( 1 + x ) λ , γ > − 1 , λ ∈ R + , where the kernel k ( x , y ) can be of different kinds. The rule, which is stable and fast convergent, is used in order to construct a computational scheme involving the single product integration rule studied in [22]. It is shown that the “compound quadrature sequence” represents an efficient proposal for saving 1/3 of the evaluations of the function f, under unchanged speed of convergence.
      PubDate: 2017-10-25T12:06:02Z
  • Stability and convergence analysis of a Crank-Nicolson leap-frog scheme
           for the unsteady incompressible Navier-Stokes equations
    • Authors: Qili Tang; Yunqing Huang
      Abstract: Publication date: Available online 12 October 2017
      Source:Applied Numerical Mathematics
      Author(s): Qili Tang, Yunqing Huang
      A fully discrete Crank-Nicolson leap-frog (CNLF) scheme is presented and studied for the nonstationary incompressible Navier-Stokes equations. The proposed scheme deals with the spatial discretization by Galerkin finite element method (FEM), treats the temporal discretization by CNLF method for the linear term and the semi-implicit method for nonlinear term. The almost unconditional stability, i.e., the time step is no more than a constant, is proven. By a new negative norm technique, the L 2 -optimal error estimates with respect to temporal and spacial orientation for the velocity are derived. At last, some numerical results are provided to justify our theoretical analysis.

      PubDate: 2017-10-18T15:25:02Z
      DOI: 10.1016/j.apnum.2017.09.012
  • On the discretization and application of two space–time boundary
           integral equations for 3D wave propagation problems in unbounded domains
    • Authors: Falletta Monegato; Scuderi
      Abstract: Publication date: February 2018
      Source:Applied Numerical Mathematics, Volume 124
      Author(s): S. Falletta, G. Monegato, L. Scuderi
      In this paper, we consider 3D wave propagation problems in unbounded domains, such as those of acoustic waves in non viscous fluids, or of seismic waves in (infinite) homogeneous isotropic materials, where the propagation velocity c is much higher than 1. For example, in the case of air and water c ≈ 343 m / s and c ≈ 1500 m / s respectively, while for seismic P-waves in linear solids we may have c ≈ 6000 m / s or higher. These waves can be generated by sources, possible away from the obstacles. We further assume that the dimensions of the obstacles are much smaller than that of the wave velocity, and that the problem transients are not excessively short. For their solution we consider two different approaches. The first directly uses a known space–time boundary integral equation to determine the problem solution. In the second one, after having defined an artificial boundary delimiting the region of computational interest, the above mentioned integral equation is interpreted as a non reflecting boundary condition to be coupled with a classical finite element method. For such problems, we show that in some cases the computational cost and storage, required by the above numerical approaches, can be significantly reduced by taking into account a property that till now has not been considered. To show the effectiveness of this reduction, the proposed approach is applied to several problems, including multiple scattering.

      PubDate: 2017-10-11T14:37:22Z
  • A Continuous hp-mesh model for adaptive discontinuous Galerkin schemes
    • Authors: Vít Dolejší; Georg May; Ajay Rangarajan
      Abstract: Publication date: Available online 2 October 2017
      Source:Applied Numerical Mathematics
      Author(s): Vít Dolejší, Georg May, Ajay Rangarajan
      We present a continuous-mesh model for anisotropic hp-adaptation in the context of numerical methods using discontinuous piecewise polynomial approximation spaces. The present work is an extension of a previously proposed mesh-only (h-)adaptation method which uses both a continuous mesh, and a corresponding high-order continuous interpolation operator. In this previous formulation local anisotropy and global mesh density distribution may be determined by analytical optimization techniques, operating on the continuous mesh model. The addition of varying polynomial degree necessitates a departure from purely analytic optimization. However, we show in this article that a global optimization problem may still be formulated and solved by analytic optimization, adding only the necessity to solve numerically a single nonlinear algebraic equation per adaptation step to satisfy a constraint on the total number of degrees of freedom. The result is a tailorsuited continuous mesh with respect to a model for the global interpolation error measured in the L q -norm. From the continuous mesh a discrete triangular mesh may be generated using any metric-based mesh generator.

      PubDate: 2017-10-03T14:25:01Z
      DOI: 10.1016/j.apnum.2017.09.015
  • Analysis of Galerkin and streamline-diffusion FEMs on piecewise
           equidistant meshes for turning point problems exhibiting an interior layer
    • Authors: Simon Becher
      Abstract: Publication date: Available online 21 September 2017
      Source:Applied Numerical Mathematics
      Author(s): Simon Becher
      We consider singularly perturbed boundary value problems with a simple interior turning point whose solutions exhibit an interior layer. These problems are discretised using higher order finite elements on layer-adapted piecewise equidistant meshes proposed by Sun and Stynes. We also study the streamline-diffusion finite element method (SDFEM) for such problems. For these methods error estimates uniform with respect to ε are proven in the energy norm and in the stronger SDFEM-norm, respectively. Numerical experiments confirm the theoretical findings.

      PubDate: 2017-09-26T13:37:25Z
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