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Computational Methods in Applied Mathematics

Editor-in-Chief: Carstensen, Carsten

Managing Editor: Matus, Piotr


IMPACT FACTOR 2018: 1.218
5-year IMPACT FACTOR: 1.411

CiteScore 2018: 1.42

SCImago Journal Rank (SJR) 2018: 0.947
Source Normalized Impact per Paper (SNIP) 2018: 0.939

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1609-9389
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Volume 14, Issue 2

Issues

Functional A Posteriori Error Estimation for Stationary Reaction-Convection-Diffusion Problems

Martin Eigel / Tatiana Samrowski
Published Online: 2014-03-13 | DOI: https://doi.org/10.1515/cmam-2014-0005

Abstract.

A functional type a posteriori error estimator for the finite element discretization of the stationary reaction-convection-diffusion equation is derived. In case of dominant convection, the solution for this class of problems typically exhibits boundary layers and shock-front like areas with steep gradients. This renders the accurate numerical solution very demanding and appropriate techniques for the adaptive resolution of regions with large approximation errors are crucial. Functional error estimators as derived here contain no mesh-dependent constants and provide guaranteed error bounds for any conforming approximation. To evaluate the error estimator, a minimization problem is solved which does not require any Galerkin orthogonality or any specific properties of the employed approximation space. Based on a set of numerical examples, we assess the performance of the new estimator. It is observed that it exhibits a good efficiency also with convection-dominated problem settings.

Keywords: A Posteriori Error Analysis; Finite Element Method; Adaptivity; Dominant Convection; Functional Estimator

MSC: 65N30; 65N15; 65J15; 65N22; 65J10

About the article

Published Online: 2014-03-13

Published in Print: 2014-04-01


Citation Information: Computational Methods in Applied Mathematics, Volume 14, Issue 2, Pages 135–150, ISSN (Online) 1609-9389, ISSN (Print) 1609-4840, DOI: https://doi.org/10.1515/cmam-2014-0005.

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