| Issue |
ESAIM: M2AN
Volume 46, Number 5, September-October 2012
|
|
|---|---|---|
| Page(s) | 1247 - 1273 | |
| DOI | https://doi.org/10.1051/m2an/2012003 | |
| Published online | 27 March 2012 | |
Adaptivity and variational stabilization for convection-diffusion equations∗
1 Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, 4 Place Jussieu, 75005 Paris, France
cohen@ann.jussieu.fr
2 Institut für Geometrie und Praktische Mathematik, RWTH Aachen, 52056 Aachen, Germany
dahmen@igpm.rwth-aachen.de; welper@igpm.rwth-aachen.de
Received: 9 August 2011
Revised: 3 December 2011
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.
Mathematics Subject Classification: 65N12 / 35J50 / 65N30
Key words: Variational problems / adaptivity / a-posteriori error estimators / stabilization
© EDP Sciences, SMAI, 2012
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