In the present paper we develop a new family of Virtual Elements for the Stokes problem on polygonal meshes. By a proper choice of the Virtual space of velocities and the associated degrees of freedom, we can guarantee that the final discrete velocity is pointwise divergence-free, and not only in a relaxed (projected) sense, as it happens for more standard elements. Moreover, we show that the discrete problem is immediately equivalent to a reduced problem with fewer degrees of freedom, thus yielding a very efficient scheme. We provide a rigorous error analysis of the method and several numerical tests, including a comparison with a different Virtual Element choice.
Beirao Da Veiga, L., Lovadina, C., & Vacca, G. (2017). Divergence free virtual elements for the stokes problem on polygonal meshes. MODÉLISATION MATHÉMATIQUE ET ANALYSE NUMÉRIQUE, 51(2), 509-535.
Citazione: | Beirao Da Veiga, L., Lovadina, C., & Vacca, G. (2017). Divergence free virtual elements for the stokes problem on polygonal meshes. MODÉLISATION MATHÉMATIQUE ET ANALYSE NUMÉRIQUE, 51(2), 509-535. |
Tipo: | Articolo in rivista - Articolo scientifico |
Carattere della pubblicazione: | Scientifica |
Presenza di un coautore afferente ad Istituzioni straniere: | No |
Titolo: | Divergence free virtual elements for the stokes problem on polygonal meshes |
Autori: | Beirao Da Veiga, L; Lovadina, C; Vacca, G |
Autori: | |
Data di pubblicazione: | 2017 |
Lingua: | English |
Rivista: | MODÉLISATION MATHÉMATIQUE ET ANALYSE NUMÉRIQUE |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1051/m2an/2016032 |
Appare nelle tipologie: | 01 - Articolo su rivista |