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Journal Articles SIAM Journal on Numerical Analysis Year : 2004

A local a posteriori error estimator based on equilibrated fluxes

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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Dates and versions

inria-00343040 , version 1 (28-11-2008)

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