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. © Springer-Verlag Berlin Heidelberg 2011.
CITATION STYLE
da Veiga, L. B., Lipnikov, K., & Manzini, G. (2011). Arbitrary order nodal mimetic discretizations of elliptic problems on polygonal meshes. Springer Proceedings in Mathematics, 4, 69–77. https://doi.org/10.1007/978-3-642-20671-9_8
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