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

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

Mathematical Citation Quotient (MCQ) 2018: 1.22

See all formats and pricing
More options …
Volume 14, Issue 2


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


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.

Export Citation

© 2014 by Walter de Gruyter Berlin/Boston.Get Permission

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

L. Tobiska and R. Verfürth
IMA Journal of Numerical Analysis, 2015, Volume 35, Number 4, Page 1652
Jikun Zhao, Shaochun Chen, Bei Zhang, and Shipeng Mao
Applied Mathematics and Computation, 2015, Volume 264, Page 346

Comments (0)

Please log in or register to comment.
Log in