A family of finite element Stokes complexes in three dimensions

08/09/2020
by   Kaibo Hu, et al.
0

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.

READ FULL TEXT

page 1

page 2

page 3

page 4

07/28/2020

Nonconforming finite element Stokes complexes in three dimensions

Two nonconforming finite element Stokes complexes ended with the nonconf...
08/14/2020

Divergence–free Scott–Vogelius elements on curved domains

We construct and analyze an isoparametric finite element pair for the St...
05/31/2021

Crouzeix-Raviart triangular elements are inf-sup stable

The Crouzeix-Raviart triangular finite elements are inf-sup stable for t...
06/06/2017

Robust and efficient validation of the linear hexahedral element

Checking mesh validity is a mandatory step before doing any finite eleme...
04/29/2022

On the Inf-Sup Stabillity of Crouzeix-Raviart Stokes Elements in 3D

We consider non-conforming discretizations of the stationary Stokes equa...
10/14/2021

Robust monolithic solvers for the Stokes-Darcy problem with the Darcy equation in primal form

We construct mesh-independent and parameter-robust monolithic solvers fo...
04/23/2021

Additive Schwarz methods for serendipity elements

While solving Partial Differential Equations (PDEs) with finite element ...