A family of finite element Stokes complexes in three dimensions [article]

Kaibo Hu and Qian Zhang and Zhimin Zhang
2021 arXiv   pre-print
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
more » ... gence-free condition. We demonstrate the validity of the algorithms by numerical experiments.
arXiv:2008.03793v2 fatcat:z4lv6xlc5zbltdqymtoitt43ei