Low-order divergence-free approximations for the Stokes problem on Worsey-Farin and Powell-Sabin splits
Numerical Analysis
2022-02-02 v1 Numerical Analysis
Abstract
We derive low-order, inf-sup stable and divergence-free finite element approximations for the Stokes problem using Worsey-Farin splits in three dimensions and Powell-Sabin splits in two dimensions. The velocity space simply consists of continuous, piecewise linear polynomials, where as the pressure space is a subspace of piecewise constants with weak continuity properties at singular edges (3D) and singular vertices (2D). We discuss implementation aspects that arise when coding the pressure space, and in particular, show that the pressure constraints can be enforced at an algebraic level.
Keywords
Cite
@article{arxiv.2105.09214,
title = {Low-order divergence-free approximations for the Stokes problem on Worsey-Farin and Powell-Sabin splits},
author = {Maurice Fabien and Johnny Guzman and Michael Neilan and Ahmed Zytoon},
journal= {arXiv preprint arXiv:2105.09214},
year = {2022}
}