Arbitrary order nodal mimetic discretizations of elliptic problems on polygonal meshes

We develop and analyze a new family of mimetic methods on unstructured polygonal meshes for the diffusion problem in primal form. The new nodal formulation that we propose in this work extends the original low-order formulation of [3] to arbitrary orders of accuracy by requiring that the consistency condition holds for polynomials of arbitrary degree m >= 1. An error estimate is presented in a mesh-dependent norm that mimics the energy norm and numerical experiments confirm the convergence rate that is expected from the theory.