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nonconforming methods

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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Residual and hierarchical a posteriori error estimatesfor nonconforming mixed finite element methods
Linda El Alaoui, Alexandre Ern
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 38 / Issue 6 / November 2004

Published online by Cambridge University Press:

15 December 2004, pp. 903-929

Print publication:

November 2004
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We analyze residual and hierarchicala posteriori error estimates for nonconforming finite elementapproximations of elliptic problems with variable coefficients.We consider a finite volume box scheme equivalent toa nonconforming mixed finite element method in a Petrov–Galerkinsetting. We prove thatall the estimators yield global upper and local lower bounds for the discretizationerror. Finally, we present results illustrating the efficiency of theestimators, for instance, in the simulation of Darcy flows throughheterogeneous porous media.