A posteriori error estimation of residual type for anisotropic diffusion-convection-reaction problems

Authors:
Thomas Apel;Serge Nicaise;Dieter Sirch
Affiliations:
Institut für Mathematik und Bauinformatik, Universität der Bundeswehr München, D-85577 Neubiberg, Germany;Université de Valenciennes et du Hainaut Cambrésis, LAMAV, ISTV, F-59313 - Valenciennes Cedex 9, France;Institut für Mathematik und Bauinformatik, Universität der Bundeswehr München, D-85577 Neubiberg, Germany
Venue:
Journal of Computational and Applied Mathematics
Year:
2011

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Abstract

This paper presents a robust a posteriori residual error estimator for diffusion-convection-reaction problems with anisotropic diffusion, approximated by a SUPG finite element method on isotropic or anisotropic meshes in R^d, d=2 or 3. The equivalence between the energy norm of the error and the residual error estimator is proved. Numerical tests confirm the theoretical results.