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

El Alaoui, Linda; Ern, Alexandre

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

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