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arXiv · 1510.01655

Divergence free Virtual Elements for the Stokes problem on polygonal meshes

L. Beirao da Veiga·C. Lovadina·G. Vacca
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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 less 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.

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L. Beirao da Veiga, C. Lovadina, G. Vacca. 2015-10-06. Divergence free Virtual Elements for the Stokes problem on polygonal meshes. https://arxiv.org/abs/1510.01655

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