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
Beirao da Veiga, L., Lovadina, C., & Russo, A. (2017). Stability analysis for the virtual element method. MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES, 27(13), 2557-2594 [10.1142/S021820251750052X].
Citazione: | Beirao da Veiga, L., Lovadina, C., & Russo, A. (2017). Stability analysis for the virtual element method. MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES, 27(13), 2557-2594 [10.1142/S021820251750052X]. | |
Tipo: | Articolo in rivista - Articolo scientifico | |
Carattere della pubblicazione: | Scientifica | |
Presenza di un coautore afferente ad Istituzioni straniere: | No | |
Titolo: | Stability analysis for the virtual element method | |
Autori: | Beirao da Veiga, L; Lovadina, C; Russo, A | |
Autori: | ||
Data di pubblicazione: | 2017 | |
Lingua: | English | |
Rivista: | MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES | |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1142/S021820251750052X | |
Appare nelle tipologie: | 01 - Articolo su rivista |
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