We analyze residual and hierarchical a posteriori error estimates for nonconforming finite element approximations of elliptic problems with variable coefficients. We consider a finite volume box scheme equivalent to a nonconforming mixed finite element method in a Petrov-Galerkin setting. We prove that all the estimators yield global upper and local lower bounds for the discretization error. Finally, we present results illustrating the efficiency of the estimators, for instance, in the simulation of Darcy flows through heterogeneous porous media.
Mots clés : finite elements, nonconforming methods, a posteriori error estimates, finite volumes, Darcy equations, heterogeneous media
@article{M2AN_2004__38_6_903_0, author = {Alaoui, Linda El and Ern, Alexandre}, title = {Residual and hierarchical a posteriori error estimates for nonconforming mixed finite element methods}, journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique}, pages = {903--929}, publisher = {EDP-Sciences}, volume = {38}, number = {6}, year = {2004}, doi = {10.1051/m2an:2004044}, mrnumber = {2108938}, zbl = {1077.65113}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an:2004044/} }
TY - JOUR AU - Alaoui, Linda El AU - Ern, Alexandre TI - Residual and hierarchical a posteriori error estimates for nonconforming mixed finite element methods JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2004 SP - 903 EP - 929 VL - 38 IS - 6 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2004044/ DO - 10.1051/m2an:2004044 LA - en ID - M2AN_2004__38_6_903_0 ER -
%0 Journal Article %A Alaoui, Linda El %A Ern, Alexandre %T Residual and hierarchical a posteriori error estimates for nonconforming mixed finite element methods %J ESAIM: Modélisation mathématique et analyse numérique %D 2004 %P 903-929 %V 38 %N 6 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2004044/ %R 10.1051/m2an:2004044 %G en %F M2AN_2004__38_6_903_0
Alaoui, Linda El; Ern, Alexandre. Residual and hierarchical a posteriori error estimates for nonconforming mixed finite element methods. ESAIM: Modélisation mathématique et analyse numérique, Tome 38 (2004) no. 6, pp. 903-929. doi : 10.1051/m2an:2004044. http://www.numdam.org/articles/10.1051/m2an:2004044/
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