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

Published online by Cambridge University Press:  15 December 2004

Linda El Alaoui  and
Alexandre Ern
Linda El Alaoui
Affiliation:
CERMICS, École nationale des ponts et chaussées, 6 et 8, avenue Blaise Pascal, 77455 Marne la Vallée Cedex 2, France. elalaoui@cermics.enpc.fr.; ern@cermics.enpc.fr.
Alexandre Ern
Affiliation:
CERMICS, École nationale des ponts et chaussées, 6 et 8, avenue Blaise Pascal, 77455 Marne la Vallée Cedex 2, France. elalaoui@cermics.enpc.fr.; ern@cermics.enpc.fr.
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Abstract

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.

Keywords

Finite elementsnonconforming methodsa posteriori error estimatesfinite volumesDarcy equationsheterogeneous media.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 38 , Issue 6 , November 2004 , pp. 903 - 929
Copyright
© EDP Sciences, SMAI, 2004

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