Arbitrary order nodal mimetic discretizations of elliptic problems on polygonal meshes with arbitrary regular solution.

We present a new family of mimetic methods on unstructured polygonal meshes for the diffusion problem in primal form for solution with regularity Cm for any integer m> 0. These methods are derived from a local consistency condition that is exact for polynomials of degree m = k + 1. The degrees of freedom are (a) solution and derivative values of various degree at the mesh vertices and (b) solution moments inside polygons. Theoretical results concerning the convergence of the method are briefly summarized and an optimal error estimate is given in a mesh-dependent norm that mimics the energy norm. Numerical experiments confirm the convergence rate that is expected from the theory.