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ARBITRARY ORDER NODAL MIMETIC DISCRETIZATIONS OF ELLIPTIC PROBLEMS ON POLYGONAL MESHES WITH ARBITRARY REGULAR SOLUTION

Veiga, L. Beirão da; Manzini, G.;

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We present a new family of mimetic methods on unstructured polygonal meshes for the diffusion problem in primal form for solution with regularity C®(­) for any integer ® ¸ 0. These methods are derived from a local consistency condition that is exact for polynomials of degree m = ® + 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.

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Palavras-chave: Diffusion problem, mimetic finite difference method, polygonal mesh, generalized mesh, high-order scheme,

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DOI: 10.5151/meceng-wccm2012-18943

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Como citar:

Veiga, L. Beirão da; Manzini, G.; "ARBITRARY ORDER NODAL MIMETIC DISCRETIZATIONS OF ELLIPTIC PROBLEMS ON POLYGONAL MESHES WITH ARBITRARY REGULAR SOLUTION", p. 2616-2628 . In: In Proceedings of the 10th World Congress on Computational Mechanics [= Blucher Mechanical Engineering Proceedings, v. 1, n. 1]. São Paulo: Blucher, 2014.
ISSN 2358-0828, DOI 10.5151/meceng-wccm2012-18943

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