Inf-sup stable finite elements on barycentric refinements producing divergence--free approximations in arbitrary dimensions
Numerical Analysis
2017-10-24 v1
Abstract
We construct several stable finite element pairs for the Stokes problem on barycentric refinements in arbitrary dimensions. A key feature of the spaces is that the divergence maps the discrete velocity space onto the the discrete pressure space; thus, when applied to models of incompressible flows, the pairs yield divergence-free velocity approximations. The key result is a local inf-sup stability that holds for any dimension and for any polynomial degree. With this result, we construct global divergence-free and stable pairs in arbitrary dimension and for any polynomial degree.
Cite
@article{arxiv.1710.08044,
title = {Inf-sup stable finite elements on barycentric refinements producing divergence--free approximations in arbitrary dimensions},
author = {Johnny Guzman and Michael Neilan},
journal= {arXiv preprint arXiv:1710.08044},
year = {2017}
}