Arbitrary-order nodal mimetic discretizations of elliptic problems on polygonal meshes

We develop and analyze a new family of mimetic finite difference methods on unstructured polygonal meshes for the diffusion problem in primal form, that use arbitrarily regular discrete spaces. The degrees of freedom are (a) solution and derivative values of various degree at suitable nodes and (b) solution moments inside polygons. Numerical experiments confirm the convergence rate that is expected from the theory.