Divergence free Virtual Elements for the Stokes problem on polygonal meshes
Numerical Analysis
2015-10-07 v1
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.
Cite
@article{arxiv.1510.01655,
title = {Divergence free Virtual Elements for the Stokes problem on polygonal meshes},
author = {L. Beirao da Veiga and C. Lovadina and G. Vacca},
journal= {arXiv preprint arXiv:1510.01655},
year = {2015}
}