We develop and analyse a new family of virtual element methods on unstructured polygonal meshes for the diffusion problem in primal form, which uses arbitrarily regular discrete spaces Vh ⊂ C α, α ∈ N. The degrees of freedom are (a) solution and derivative values of various degrees at suitable nodes and (b) solution moments inside polygons. The convergence of the method is proved theoretically and an optimal error estimate is derived. Numerical experiments confirm the convergence rate that is expected from the theory. © 2014 Published by Oxford University Press.

BEIRAO DA VEIGA, L., Manzini, G. (2014). A virtual element method with arbitrary regularity. IMA JOURNAL OF NUMERICAL ANALYSIS, 34(2), 759-781 [10.1093/imanum/drt018].

A virtual element method with arbitrary regularity

BEIRAO DA VEIGA, LOURENCO
Primo
;
2014

Abstract

We develop and analyse a new family of virtual element methods on unstructured polygonal meshes for the diffusion problem in primal form, which uses arbitrarily regular discrete spaces Vh ⊂ C α, α ∈ N. The degrees of freedom are (a) solution and derivative values of various degrees at suitable nodes and (b) solution moments inside polygons. The convergence of the method is proved theoretically and an optimal error estimate is derived. Numerical experiments confirm the convergence rate that is expected from the theory. © 2014 Published by Oxford University Press.
Articolo in rivista - Articolo scientifico
Virtual Elements
English
2014
34
2
759
781
none
BEIRAO DA VEIGA, L., Manzini, G. (2014). A virtual element method with arbitrary regularity. IMA JOURNAL OF NUMERICAL ANALYSIS, 34(2), 759-781 [10.1093/imanum/drt018].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/98397
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