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

Cockburn, Bernardo; Zhang, Wujun

doi:10.1090/S0025-5718-2013-02789-5

An a posteriori error estimate for the variable-degree Raviart-Thomas method
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by Bernardo Cockburn and Wujun Zhang PDF

Math. Comp. 83 (2014), 1063-1082 Request permission

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 $L_2$-norm of the error of the flux. We also find the explicit dependence of the estimator on the order of the local spaces $k\ge 0$; 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 $k$.

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