We develop and analyze a new family of mimetic methods on unstructured polygonal meshes for the diffusion problem in primal form. These methods are derived from the local consistency condition that is exact for polynomials of any degree $m\geq1$. The degrees of freedom are (a) solution values at the quadrature nodes of the Gauss–Lobatto formulas on each mesh edge, and (b) solution moments inside polygons. The convergence of the method is proven theoretically and an optimal error estimate is derived in a mesh-dependent norm that mimics the energy norm. Numerical experiments confirm the convergence rate that is expected from the theory.

BEIRAO DA VEIGA, L., Lipnikov, K., Manzini, G. (2011). Arbitrary-order nodal mimetic discretizations of elliptic problems on polygonal meshes. SIAM JOURNAL ON NUMERICAL ANALYSIS, 49(5), 1737-1760 [10.1137/100807764].

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

BEIRAO DA VEIGA, LOURENCO
Primo
;
2011

Abstract

We develop and analyze a new family of mimetic methods on unstructured polygonal meshes for the diffusion problem in primal form. These methods are derived from the local consistency condition that is exact for polynomials of any degree $m\geq1$. The degrees of freedom are (a) solution values at the quadrature nodes of the Gauss–Lobatto formulas on each mesh edge, and (b) solution moments inside polygons. The convergence of the method is proven theoretically and an optimal error estimate is derived in a mesh-dependent norm that mimics the energy norm. Numerical experiments confirm the convergence rate that is expected from the theory.
Articolo in rivista - Articolo scientifico
mimetic discretization
English
1737
1760
24
BEIRAO DA VEIGA, L., Lipnikov, K., Manzini, G. (2011). Arbitrary-order nodal mimetic discretizations of elliptic problems on polygonal meshes. SIAM JOURNAL ON NUMERICAL ANALYSIS, 49(5), 1737-1760 [10.1137/100807764].
BEIRAO DA VEIGA, L; Lipnikov, K; Manzini, G
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/98841
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