An a posteriori error estimate for the variable-degree Raviart-Thomas method

Bernardo Cockburn, Wujun Zhang

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10 Scopus citations

Abstract

We propose a new a posteriori error analysis of the variable-degree, hybridized version of the Raviart-Thomas method for second-order elliptic problems on conforming meshes made of simplexes. We establish both the reliability and efficiency of the estimator for the L2-norm of the error of the flux. We also find the explicit dependence of the estimator on the order of the local spaces k ≥ 0; the only constants that are not explicitly computed are those depending on the shape-regularity of the simplexes. In particular, the constant of the local efficiency inequality is proven to behave like (k + 2)3/2. However, we present numerical experiments suggesting that such a constant is actually independent of k.

Original languageEnglish (US)
Pages (from-to)1063-1082
Number of pages20
JournalMathematics of Computation
Volume83
Issue number287
DOIs
StatePublished - May 1 2014

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