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DOE OSTI · 1331260

Conforming and nonconforming virtual element methods for elliptic problems

Cangiani, Andrea·Manzini, Gianmarco·Sutton, Oliver J.
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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 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.

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97 MATHEMATICS AND COMPUTINGconvection-diffusion-reaction equationselliptic problemsmathematicspolygonal and polyhedral meshesvirtual element methods

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Cangiani, Andrea, Manzini, Gianmarco, Sutton, Oliver J.. 2016-08-03. Conforming and nonconforming virtual element methods for elliptic problems. https://doi.org/10.1093/imanum%2Fdrw036

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