Residual and hierarchical a posteriori error estimates for nonconforming mixed finite element methods

Alaoui, Linda El; Ern, Alexandre

doi:10.1051/m2an:2004044

Alaoui, Linda El ; Ern, Alexandre

ESAIM: Modélisation mathématique et analyse numérique, Tome 38 (2004) no. 6, pp. 903-929.

Résumé

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.

MR Zbl | 1 citation dans Numdam

DOI : 10.1051/m2an:2004044

Classification : 65N15, 65N60, 75N12, 76905
Mots clés : finite elements, nonconforming methods, a posteriori error estimates, finite volumes, Darcy equations, heterogeneous media

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     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://archive.numdam.org/articles/10.1051/m2an:2004044/}
}

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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://archive.numdam.org/articles/10.1051/m2an:2004044/

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