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Adaptivity and variational stabilization for convection-diffusion equations

Published online by Cambridge University Press:  27 March 2012

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.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2012

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