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Computational Methods in Applied Mathematics

Editor-in-Chief: Carstensen, Carsten

Managing Editor: Matus, Piotr

4 Issues per year


IMPACT FACTOR 2016: 1.097

CiteScore 2016: 1.09

SCImago Journal Rank (SJR) 2016: 0.872
Source Normalized Impact per Paper (SNIP) 2016: 0.887

Mathematical Citation Quotient (MCQ) 2016: 0.75

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1609-9389
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Volume 15, Issue 4 (Oct 2015)

Issues

Some Open Questions in the Numerical Analysis of Singularly Perturbed Differential Equations

Hans-Görg Roos / Martin Stynes
  • Corresponding author
  • Beijing Computational Science Research Center, Haidian District, Beijing, China; and Department of Mathematics, National University of Ireland, Cork, Ireland
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Published Online: 2015-06-16 | DOI: https://doi.org/10.1515/cmam-2015-0011

Abstract

Several open questions in the numerical analysis of singularly perturbed differential equations are discussed. These include whether certain convergence results in various norms are optimal, when supercloseness is obtained in finite element solutions, the validity of defect correction in finite difference approximations, and desirable adaptive mesh refinement results that remain to be proved or disproved.

Keywords: Singularly Perturbed; Convection-Diffusion; Reaction-Diffusion

MSC: 65-02

The authors would like to thank Natalia Kopteva and Martin Schopf for helpful discussions related to this paper. We are also grateful to the referees for their careful reading of the paper and their useful comments.

About the article

Received: 2014-11-04

Revised: 2015-03-10

Accepted: 2015-04-07

Published Online: 2015-06-16

Published in Print: 2015-10-01


Citation Information: Computational Methods in Applied Mathematics, ISSN (Online) 1609-9389, ISSN (Print) 1609-4840, DOI: https://doi.org/10.1515/cmam-2015-0011.

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