Residual and hierarchical a posteriori error estimates for nonconforming mixed finite element methods
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 38 (2004) no. 6, p. 903-929

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.

DOI : https://doi.org/10.1051/m2an:2004044
Classification:  65N15,  65N60,  75N12,  76905
Keywords: 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: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {38},
     number = {6},
     year = {2004},
     pages = {903-929},
     doi = {10.1051/m2an:2004044},
     zbl = {1077.65113},
     mrnumber = {2108938},
     language = {en},
     url = {http://www.numdam.org/item/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: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 38 (2004) no. 6, pp. 903-929. doi : 10.1051/m2an:2004044. http://www.numdam.org/item/M2AN_2004__38_6_903_0/

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