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Medientyp:
E-Artikel
Titel:
Stability analysis for the virtual element method
Beteiligte:
Beirão da Veiga, Lourenço;
Lovadina, Carlo;
Russo, Alessandro
Erschienen:
World Scientific Pub Co Pte Ltd, 2017
Erschienen in:Mathematical Models and Methods in Applied Sciences
Sprache:
Englisch
DOI:
10.1142/s021820251750052x
ISSN:
0218-2025;
1793-6314
Entstehung:
Anmerkungen:
Beschreibung:
<jats:p> 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. </jats:p>