A Local A Posteriori Error Estimator Based on Equilibrated Fluxes

Authors:
R. Luce;B. I. Wohlmuth
Affiliations:
-;-
Venue:
SIAM Journal on Numerical Analysis
Year:
2004

Citing 0
Cited 12

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Flux reconstruction for the P2 nonconforming finite element method with application to a posteriori error estimation

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On the asymptotic exactness of error estimators based on the equilibrated residual method for quadrilateral finite elements

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Computational survey on a posteriori error estimators for nonconforming finite element methods for the Poisson problem

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Abstract

We present and analyze a new a posteriori error estimator for lowest order conforming finite elements. It is based on Raviart--Thomas finite elements and can be obtained locally by a postprocessing technique involving for each vertex a local subproblem associated with a dual mesh. Under certain regularity assumptions on the right-hand side, we obtain an error estimator where the constant in the upper bound for the true error tends to one. Replacing the conforming finite element solution by a postprocessed one, the error estimator is asymptotically exact. The local equivalence between our estimator and the standard residual-based error estimator is established. Numerical results illustrate the performance of the error estimator.