Conforming and nonconforming virtual element methods for elliptic problems

Cangiani, Andrea; Manzini, Gianmarco; Sutton, Oliver J.

doi:10.1093/imanum/drw036

Title: Conforming and nonconforming virtual element methods for elliptic problems

Journal Article · Wed Aug 03 00:00:00 EDT 2016 · IMA Journal of Numerical Analysis

DOI:https://doi.org/10.1093/imanum/drw036· OSTI ID:1331260

Cangiani, Andrea ^[1]; Manzini, Gianmarco ^[2]; Sutton, Oliver J. ^[1]

Univ. of Leicester, Leicester (United Kingdom)
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Here we present, in a unified framework, new conforming and nonconforming virtual element methods for general second-order elliptic problems in two and three dimensions. The differential operator is split into its symmetric and nonsymmetric parts and conditions for stability and accuracy on their discrete counterparts are established. These conditions are shown to lead to optimal H¹- and L²-error estimates, confirmed by numerical experiments on a set of polygonal meshes. The accuracy of the numerical approximation provided by the two methods is shown to be comparable.

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Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE Laboratory Directed Research and Development (LDRD) Program

Grant/Contract Number:: AC52-06NA25396

OSTI ID:: 1331260

Report Number(s):: LA-UR-15-23951

Journal Information:: IMA Journal of Numerical Analysis, Journal Name: IMA Journal of Numerical Analysis; ISSN 0272-4979

Publisher:: Oxford University Press/Institute of Mathematics and its ApplicationsCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 155 works

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On the virtual element method for topology optimization on polygonal meshes: A numerical study Antonietti, P. F.; Bruggi, M.; Scacchi, S. Computers & Mathematics with Applications, Vol. 74, Issue 5 https://doi.org/10.1016/j.camwa.2017.05.025	journal	September 2017
The Virtual Element Method in 50 lines of MATLAB Sutton, Oliver J. arXiv https://doi.org/10.48550/arxiv.1604.06021	preprint	January 2016
Virtual Element Method for Second Order Elliptic Eigenvalue Problems Gardini, Francesca; Vacca, Giuseppe arXiv https://doi.org/10.48550/arxiv.1610.03675	preprint	January 2016
Exponential convergence of the hp Virtual Element Method with corner singularities Mascotto, Lorenzo; da Veiga, Lourenço Beirão; Chernov, Alexey arXiv https://doi.org/10.48550/arxiv.1611.10165	preprint	January 2016

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