Conforming and nonconforming virtual element methods for elliptic problems
Here we present, in a unified framework, new conforming and nonconforming virtual element methods for general secondorder 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 H ^{1} and L ^{2}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:

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 Univ. of Leicester, Leicester (United Kingdom)
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Publication Date:
 Report Number(s):
 LAUR1523951
Journal ID: ISSN 02724979
 Grant/Contract Number:
 AC5206NA25396
 Type:
 Accepted Manuscript
 Journal Name:
 IMA Journal of Numerical Analysis
 Additional Journal Information:
 Journal Name: IMA Journal of Numerical Analysis; Journal ID: ISSN 02724979
 Publisher:
 Oxford University Press/Institute of Mathematics and its Applications
 Research Org:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org:
 USDOE Laboratory Directed Research and Development (LDRD) Program
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; mathematics; elliptic problems; virtual element methods; polygonal and polyhedral meshes; convectiondiffusionreaction equations
 OSTI Identifier:
 1331260
Cangiani, Andrea, Manzini, Gianmarco, and Sutton, Oliver J. Conforming and nonconforming virtual element methods for elliptic problems. United States: N. p.,
Web. doi:10.1093/imanum/drw036.
Cangiani, Andrea, Manzini, Gianmarco, & Sutton, Oliver J. Conforming and nonconforming virtual element methods for elliptic problems. United States. doi:10.1093/imanum/drw036.
Cangiani, Andrea, Manzini, Gianmarco, and Sutton, Oliver J. 2016.
"Conforming and nonconforming virtual element methods for elliptic problems". United States.
doi:10.1093/imanum/drw036. https://www.osti.gov/servlets/purl/1331260.
@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 secondorder 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 L2error 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 = {2016},
month = {8}
}