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Conforming and nonconforming virtual element methods for elliptic problems

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journal contribution
posted on 2016-11-11, 14:31 authored by Andrea Cangiani, G. Manzini, Oliver J. Sutton
We present in a unified framework new conforming and nonconforming Virtual Element Methods (VEM) for general second order elliptic problems in two and three dimensions. The differential operator is split into its symmetric and non-symmetric 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.

Funding

EPSRC (Grant EP/L022745/1) to A.C.; Laboratory Directed Research and Development program (LDRD), US Department of Energy Office of Science, Office of Fusion Energy Sciences, under the auspices of the National Nuclear Security Administration of the US Department of Energy by Los Alamos National Laboratory, operated by Los Alamos National Security LLC under contract DE-AC52- 06NA25396 to G.M.; Ph.D. Studentship from the College of Science and Engineering at the University of Leicester and an EPSRC Doctoral Training Grant to O.S.

History

Citation

IMA Journal of Numerical Analysis (2017) 37 (3): 1317-1354.

Author affiliation

/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Mathematics

Version

  • AM (Accepted Manuscript)

Published in

IMA Journal of Numerical Analysis (2017) 37 (3): 1317-1354.

Publisher

Oxford University Press (OUP) for Institute of Mathematics and its Applications

issn

0272-4979

eissn

1464-3642

Acceptance date

2016-02-22

Copyright date

2016

Available date

2017-08-03

Publisher version

http://imajna.oxfordjournals.org/content/early/2016/08/03/imanum.drw036

Language

en

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