Journal
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
Volume 27, Issue 13, Pages 2557-2594Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S021820251750052X
Keywords
Virtual element methods; stability analysis; convergence analysis
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Funding
- European Research Council through the H Consolidator Grant [681162]
- University of Milano-Bicocca
- IMATI-CNR
- European Research Council (ERC) [681162] Funding Source: European Research Council (ERC)
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We analyze the virtual element methods (VEM) on a simple elliptic model problem, allowing for more general meshes than the one typically considered in the VEM literature. For instance, meshes with arbitrarily small edges (with respect to the parent element diameter) can be dealt with. Our general approach applies to different choices of the stability form, including, for example, the classical one introduced in Ref. 4, and a recent one presented in Ref. 34. Finally, we show that the stabilization term can be simplified by dropping the contribution of the internal-to-the-element degrees of freedom. The resulting stabilization form, involving only the boundary degrees of freedom, can be used in the VEM scheme without affecting the stability and convergence properties. The numerical tests are in accordance with the theoretical predictions.
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