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A local a posteriori error estimator based on equilibrated fluxes

Robert Luce 1, 2 B.I. Wohlmuth 3
1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
2 CONCHA - Complex Flow Simulation Codes based on High-order and Adaptive methods
Inria Bordeaux - Sud-Ouest, UPPA - Université de Pau et des Pays de l'Adour, CNRS - Centre National de la Recherche Scientifique : UMR5142
3 IANS - Institut für Angewandte Analysis und Numerische Simulation [Stuttgart]
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.
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https://hal.inria.fr/inria-00343040
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Submitted on : Friday, November 28, 2008 - 6:48:08 PM
Last modification on : Thursday, February 11, 2021 - 2:40:03 PM

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CNRS | INRIA | UNIV-PAU | LMA-PAU | INSMI

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Robert Luce, B.I. Wohlmuth. A local a posteriori error estimator based on equilibrated fluxes. SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2004, 42 (4), pp.1394-1414. ⟨10.1137/S0036142903433790⟩. ⟨inria-00343040⟩

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