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.
Mots-clés : variational problems, adaptivity, a-posteriori error estimators, stabilization
@article{M2AN_2012__46_5_1247_0, author = {Cohen, Albert and Dahmen, Wolfgang and Welper, Gerrit}, title = {Adaptivity and variational stabilization for convection-diffusion equations}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis }, pages = {1247--1273}, publisher = {EDP-Sciences}, volume = {46}, number = {5}, year = {2012}, doi = {10.1051/m2an/2012003}, mrnumber = {2916380}, zbl = {1270.65065}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an/2012003/} }
TY - JOUR AU - Cohen, Albert AU - Dahmen, Wolfgang AU - Welper, Gerrit TI - Adaptivity and variational stabilization for convection-diffusion equations JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2012 SP - 1247 EP - 1273 VL - 46 IS - 5 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2012003/ DO - 10.1051/m2an/2012003 LA - en ID - M2AN_2012__46_5_1247_0 ER -
%0 Journal Article %A Cohen, Albert %A Dahmen, Wolfgang %A Welper, Gerrit %T Adaptivity and variational stabilization for convection-diffusion equations %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2012 %P 1247-1273 %V 46 %N 5 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2012003/ %R 10.1051/m2an/2012003 %G en %F M2AN_2012__46_5_1247_0
Cohen, Albert; Dahmen, Wolfgang; Welper, Gerrit. Adaptivity and variational stabilization for convection-diffusion equations. ESAIM: Mathematical Modelling and Numerical Analysis , Volume 46 (2012) no. 5, pp. 1247-1273. doi : 10.1051/m2an/2012003. http://www.numdam.org/articles/10.1051/m2an/2012003/
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