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Title: 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 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 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:
 [1] ;  [2] ;  [1]
  1. Univ. of Leicester, Leicester (United Kingdom)
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Report Number(s):
LA-UR-15-23951
Journal ID: ISSN 0272-4979
Grant/Contract Number:
AC52-06NA25396
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
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; convection-diffusion-reaction 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 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 = {2016},
month = {8}
}