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

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 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 ≥ 0 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 (k+{2})^{3/2} . However, we present numerical experiments suggesting that such a constant is actually independent of k k .