An a-posteriori error estimator for the mimetic finite difference approximation of elliptic problems

We present an a posteriori error indicator for the mimetic finite difference approximation of elliptic problems in the mixed form. We show that this estimator is reliable and efficient with respect to an energy-type error comprising both flux and pressure. Its performance is investigated by numerically solving the diffusion equation on computational domains with different shapes, different permeability tensors, and different types of computational meshes. Copyright