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 ⊂ Cα, 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.

A virtual element method with arbitrary regularity / L. Beirao da Veiga, G. Manzini. - In: IMA JOURNAL OF NUMERICAL ANALYSIS. - ISSN 0272-4979. - 34:2(2014), pp. 759-781.

A virtual element method with arbitrary regularity

L. Beirao da Veiga
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 ⊂ Cα, 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.
Settore MAT/08 - Analisi Numerica
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/246916
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