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Computational Methods in Applied Mathematics

Editor-in-Chief: Carstensen, Carsten

Managing Editor: Matus, Piotr

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Volume 15, Issue 4


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


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, Volume 15, Issue 4, Pages 531–550, ISSN (Online) 1609-9389, ISSN (Print) 1609-4840, DOI: https://doi.org/10.1515/cmam-2015-0011.

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