Residual and hierarchical a posteriori error estimates for nonconforming mixed finite element methods
Alaoui, Linda El ; Ern, Alexandre
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 38 (2004), p. 903-929 / Harvested from Numdam
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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.

Publié le : 2004-01-01
DOI : https://doi.org/10.1051/m2an:2004044
Classification:  65N15,  65N60,  75N12,  76905 
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     author = {Alaoui, Linda El and Ern, Alexandre},
     title = {Residual and hierarchical a posteriori error estimates for nonconforming mixed finite element methods},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {38},
     year = {2004},
     pages = {903-929},
     doi = {10.1051/m2an:2004044},
     mrnumber = {2108938},
     zbl = {1077.65113},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_2004__38_6_903_0}
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Alaoui, Linda El; Ern, Alexandre. Residual and hierarchical a posteriori error estimates for nonconforming mixed finite element methods. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 38 (2004) pp. 903-929. doi : 10.1051/m2an:2004044. http://gdmltest.u-ga.fr/item/M2AN_2004__38_6_903_0/

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