Adaptivity and variational stabilization for convection-diffusion equations
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 46 (2012) no. 5, p. 1247-1273

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.

DOI : https://doi.org/10.1051/m2an/2012003
Classification:  65N12,  35J50,  65N30
Keywords: 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 - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {46},
     number = {5},
     year = {2012},
     pages = {1247-1273},
     doi = {10.1051/m2an/2012003},
     zbl = {1270.65065},
     mrnumber = {2916380},
     language = {en},
     url = {http://www.numdam.org/item/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 - Modélisation Mathématique et Analyse Numérique, Volume 46 (2012) no. 5, pp. 1247-1273. doi : 10.1051/m2an/2012003. http://www.numdam.org/item/M2AN_2012__46_5_1247_0/

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