A family of finite element Stokes complexes in three dimensions
Numerical Analysis
2021-11-02 v2 Numerical Analysis
Abstract
We construct finite element Stokes complexes on tetrahedral meshes in three-dimensional space. In the lowest order case, the finite elements in the complex have 4, 18, 16, and 1 degrees of freedom, respectively. As a consequence, we obtain gradcurl-conforming finite elements and inf-sup stable Stokes pairs on tetrahedra which fit into complexes. We show that the new elements lead to convergent algorithms for solving a gradcurl model problem as well as solving the Stokes system with precise divergence-free condition. We demonstrate the validity of the algorithms by numerical experiments.
Keywords
Cite
@article{arxiv.2008.03793,
title = {A family of finite element Stokes complexes in three dimensions},
author = {Kaibo Hu and Qian Zhang and Zhimin Zhang},
journal= {arXiv preprint arXiv:2008.03793},
year = {2021}
}
Comments
27 pages, 1 figure