Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Computational Methods in Applied Mathematics

Editor-in-Chief: Carstensen, Carsten

Managing Editor: Matus, Piotr

4 Issues per year

IMPACT FACTOR 2017: 0.658

CiteScore 2017: 1.05

SCImago Journal Rank (SJR) 2017: 1.291
Source Normalized Impact per Paper (SNIP) 2017: 0.893

Mathematical Citation Quotient (MCQ) 2017: 0.76

See all formats and pricing
More options …
Volume 18, Issue 2


A Short Note on the Connection Between Layer-Adapted Exponentially Graded and S-Type Meshes

Sebastian Franz / Christos Xenophontos
Published Online: 2017-07-06 | DOI: https://doi.org/10.1515/cmam-2017-0020


In this short note we analyse a connection between the exponentially graded and a generalisation of the class of S-type meshes for singularly perturbed problems.

Keywords: Singular Perturbation; Boundary Layers; Layer-Adapted Meshes

MSC 2010: 65N12; 65N30; 65N50


  • [1]

    N. S. Bakhvalov, The optimization of methods of solving boundary value problems with a boundary layer, USSR Comput. Math. Math. Phys. 9 (1969), no. 4, 139–166. CrossrefGoogle Scholar

  • [2]

    P. Constantinou and C. Xenophontos, Finite element analysis of an exponentially graded mesh for singularly perturbed problems, Comput. Methods Appl. Math. 15 (2015), no. 2, 135–143. Web of ScienceGoogle Scholar

  • [3]

    S. Franz, L. Ludwig and C. Xenophontos, Finite element approximation of convection-diffusion problems using an exponentially graded mesh, Comput. Math. Appl. 72 (2016), no. 6, 1532–1540. CrossrefWeb of ScienceGoogle Scholar

  • [4]

    S. Franz, L. Ludwig and C. Xenophontos, Finite element approximation of reaction-diffusion problems using an exponentially graded mesh, in preparation.

  • [5]

    T. Linß, Analysis of a Galerkin finite element method on a Bakhvalov–Shishkin mesh for a linear convection-diffusion problem, IMA J. Numer. Anal. 20 (2000), no. 4, 621–632. CrossrefGoogle Scholar

  • [6]

    T. Linß, Layer-Adapted Meshes for Reaction-Convection-Diffusion Problems, Lecture Notes in Math. 1985, Springer, Berlin, 2010. Google Scholar

  • [7]

    H.-G. Roos and T. Linß, Sufficient conditions for uniform convergence on layer-adapted grids, Computing 63 (1999), 27–45. CrossrefGoogle Scholar

  • [8]

    H.-G. Roos, M. Stynes and L. Tobiska, Robust Numerical Methods for Singularly Perturbed Differential Equations, 2nd ed., Springer Ser. Comput. Math. 24, Springer, Berlin, 2008. Google Scholar

  • [9]

    H.-G. Roos, L. Teofanov and Z. Uzelac, Graded meshes for high order FEM, J. Comput. Math. 33 (2015), no. 1, 1–16. CrossrefGoogle Scholar

  • [10]

    G. Shishkin, Grid approximation of singularly perturbed elliptic and parabolic equations (in Russian), Second doctorial thesis, Keldysh Institute, Moscow, 1990. Google Scholar

  • [11]

    M. van Veldhuizen, Higher order methods for a singularly perturbed problem, Numer. Math. 30 (1978), 267–279. CrossrefGoogle Scholar

  • [12]

    C. Xenophontos, Optimal mesh design for the finite element approximation of reaction-diffusion problems, Internat. J. Numer. Methods Engrg. 53 (2002), 929–943. CrossrefGoogle Scholar

  • [13]

    C. Xenophontos, A parameter robust finite element method for fourth order singularly perturbed problems, Comput. Methods Appl. Math. 17 (2017), no. 2, 337–349. Web of ScienceGoogle Scholar

About the article

Received: 2017-04-15

Revised: 2017-05-29

Accepted: 2017-06-16

Published Online: 2017-07-06

Published in Print: 2018-04-01

Citation Information: Computational Methods in Applied Mathematics, Volume 18, Issue 2, Pages 199–202, ISSN (Online) 1609-9389, ISSN (Print) 1609-4840, DOI: https://doi.org/10.1515/cmam-2017-0020.

Export Citation

© 2018 Walter de Gruyter GmbH, Berlin/Boston.Get Permission

Comments (0)

Please log in or register to comment.
Log in