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  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.
Keywordsmimetic finite difference diffusion problems unstructured mesh polygonal element
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The work of the second author was supported by the Department of Energy (DOE) Advanced Scientific Computing Research (ASCR) program in Applied Mathematics. The work of the third author was partially supported by the Italian MIUR through the program PRIN2008.
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