Flux reconstruction and solution post-processing in mimetic finite difference methods

We present a post-processing technique for the mimetic finite difference solution of diffusion problems in mixed form. Our post-processing method yields a piecewise linear approximation of the scalar variable that is second-order accurate in the L2-norm on quite general polyhedral meshes, including non-convex and non-matching elements. The post-processing is based on the reconstruction of vector fields projected onto the mimetic space of vector variables. This technique is exact on constant vector fields and is shown to be independent of the mimetic scalar product choice if a local consistency condition is satisfied. The post-processing method is computationally inexpensive. Optimal performance is confirmed by numerical experiments.