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

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.