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|Title:||Conforming and nonconforming virtual element methods for elliptic problems|
Sutton, Oliver J.
|Publisher:||Oxford University Press (OUP) for Institute of Mathematics and its Applications|
|Citation:||IMA Journal of Numerical Analysis (2017) 37 (3): 1317-1354.|
|Abstract:||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.|
|Rights:||© The authors 2016. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved. Archived with reference to SHERPA/RoMEO and publisher website.|
|Appears in Collections:||Published Articles, Dept. of Mathematics|
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