Divergence--free Scott--Vogelius elements on curved domains
Numerical Analysis
2020-08-17 v1 Numerical Analysis
Abstract
We construct and analyze an isoparametric finite element pair for the Stokes problem in two dimensions. The pair is defined by mapping the Scott-Vogelius finite element space via a Piola transform. The velocity space has the same degrees of freedom as the quadratic Lagrange finite element space, and therefore the proposed spaces reduce to the Scott-Vogelius pair in the interior of the domain. We prove that the resulting method converges with optimal order, is divergence--free, and is pressure robust. Numerical examples are provided which support the theoretical results.
Cite
@article{arxiv.2008.06429,
title = {Divergence--free Scott--Vogelius elements on curved domains},
author = {Michael Neilan and M. Baris Otus},
journal= {arXiv preprint arXiv:2008.06429},
year = {2020}
}