Data di Pubblicazione:
2017
Citazione:
Divergence free virtual elements for the stokes problem on polygonal meshes / L.B. Da Veiga, C. Lovadina, G. Vacca. - In: MODÉLISATION MATHÉMATIQUE ET ANALYSE NUMÉRIQUE. - ISSN 0764-583X. - 51:2(2017), pp. 509-535.
Abstract:
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.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Divergence free approximation; Polygonal meshes; Stokes problem; Virtual element method; Analysis; Numerical Analysis; Modeling and Simulation; Applied Mathematics
Elenco autori:
L.B. Da Veiga, C. Lovadina, G. Vacca
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