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Adaptivity and variational stabilization for convection-diffusion equations∗

Published online by Cambridge University Press:  27 March 2012

Albert Cohen ,
Wolfgang Dahmen  and
Gerrit Welper
Albert Cohen
Affiliation:
Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, 4 Place Jussieu, 75005 Paris, France. cohen@ann.jussieu.fr
Wolfgang Dahmen
Affiliation:
Institut für Geometrie und Praktische Mathematik, RWTH Aachen, 52056 Aachen, Germany; dahmen@igpm.rwth-aachen.de; welper@igpm.rwth-aachen.de
Gerrit Welper
Affiliation:
Institut für Geometrie und Praktische Mathematik, RWTH Aachen, 52056 Aachen, Germany; dahmen@igpm.rwth-aachen.de; welper@igpm.rwth-aachen.de
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Abstract

In this paper we propose and analyze stable variational formulations for convection diffusion problems starting from concepts introduced by Sangalli. We derive efficient and reliable a posteriori error estimators that are based on these formulations. The analysis of resulting adaptive solution concepts, when specialized to the setting suggested by Sangalli’s work, reveals partly unexpected phenomena related to the specific nature of the norms induced by the variational formulation. Several remedies, based on other specifications, are explored and illustrated by numerical experiments.

Keywords

Variational problemsadaptivitya-posteriori error estimatorsstabilization
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 46 , Issue 5 , September 2012 , pp. 1247 - 1273
Copyright
© EDP Sciences, SMAI, 2012

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