Volume 38, Number 6, November-December 2004
|Page(s)||903 - 929|
|Published online||15 December 2004|
Residual and hierarchical a posteriori error estimates for nonconforming mixed finite element methods
CERMICS, École nationale des ponts et chaussées, 6 et 8, avenue Blaise Pascal, 77455 Marne la
Vallée Cedex 2, France. firstname.lastname@example.org.; email@example.com.
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.
Mathematics Subject Classification: 65N15 / 65N60 / 75N12 / 76905
Key words: Finite elements / nonconforming methods / a posteriori error estimates / finite volumes / Darcy equations / heterogeneous media.
© EDP Sciences, SMAI, 2004
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