A residual based error estimator for the mimetic finite difference method

We present a local error indicator for the Mimetic Finite Difference method for diffusion-type problems on polyhedral meshes. Under essentially the same general hypotheses used in (SIAM J. Numer. Anal. 43:1872-1896, 2005) to show the convergence of the method, we prove the global reliability and local efficiency of the proposed estimator.