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

Abstract

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.

Authors:

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)

Publication Date:: Wed Aug 03 00:00:00 EDT 2016

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

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

OSTI Identifier:: 1331260

Report Number(s):: LA-UR-15-23951
Journal ID: ISSN 0272-4979

Grant/Contract Number:: AC52-06NA25396

Resource Type:: Accepted Manuscript

Journal Name:: IMA Journal of Numerical Analysis

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

Publisher:: Oxford University Press/Institute of Mathematics and its Applications

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; mathematics; elliptic problems; virtual element methods; polygonal and polyhedral meshes; convection-diffusion-reaction equations

Citation Formats


                    Cangiani, Andrea, Manzini, Gianmarco, and Sutton, Oliver J. Conforming and nonconforming virtual element methods for elliptic problems.  United States: N. p., 2016. 
Web.  doi:10.1093/imanum/drw036.

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                    Cangiani, Andrea, Manzini, Gianmarco, & Sutton, Oliver J. Conforming and nonconforming virtual element methods for elliptic problems.  United States.  https://doi.org/10.1093/imanum/drw036

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                    Cangiani, Andrea, Manzini, Gianmarco, and Sutton, Oliver J. Wed .  
"Conforming and nonconforming virtual element methods for elliptic problems".  United States.  https://doi.org/10.1093/imanum/drw036.  https://www.osti.gov/servlets/purl/1331260.

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@article{osti_1331260,

  title        = {Conforming and nonconforming virtual element methods for elliptic problems},

  author       = {Cangiani, Andrea and Manzini, Gianmarco and Sutton, Oliver J.},

  abstractNote = {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.},

  doi          = {10.1093/imanum/drw036},

  journal      = {IMA Journal of Numerical Analysis},

  number       = ,

  volume       = ,

  place        = {United States},

  year         = {Wed Aug 03 00:00:00 EDT 2016},

  month        = {Wed Aug 03 00:00:00 EDT 2016}

}

Copy to clipboard

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Works referencing / citing this record:

A third Strang lemma and an Aubin–Nitsche trick for schemes in fully discrete formulation
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Di Pietro, Daniele A.; Droniou, Jérôme
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Virtual Element Method for Second Order Elliptic Eigenvalue Problems
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Exponential convergence of the hp Virtual Element Method with corner singularities
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Title: Conforming and nonconforming virtual element methods for elliptic problems

Abstract

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A Stream Virtual Element Formulation of the Stokes Problem on Polygonal Meshes
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Generalized Finite Element Methods: Their Performance and Their Relation to Mixed Methods
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hp-Version discontinuous Galerkin methods on polygonal and polyhedral meshes
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