A family of finite element stokes complexes in three dimensions

Journal article

We construct finite element Stokes complexes on tetrahedral meshes. In the lowest-order case, the finite elements in the complex have 4, 18, 16, and 1 degrees of freedom on each tetrahedron, respectively. As a consequence, we obtain grad curl-conforming finite elements and inf-sup stable Stokes pairs on tetrahedral meshes which fit into complexes. We show that the new elements lead to convergent algorithms for solving a grad curl model problem as well as solving the Stokes system with precise divergence-free condition. As a by-product, we obtain some nonconforming elements for the grad curl model problem. We demonstrate the validity of the nonconforming elements by numerical experiments.

Authors: Hu, K; Zhang, Q; Zhang, Z

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Society for Industrial and Applied Mathematics
• Journal: SIAM Journal on Numerical Analysis
• Volume: 60
• Issue: 1
• Pages: 222-243
• Publication date: 2022-01-25
• Acceptance date: 2021-10-21
• DOI: 10.1137/20m1358700
• EISSN: 1095-7170
• ISSN: 0036-1429
• Language: English
• Keywords: grad curl-conforming; finite elements; Stokes complexes; divergence free; curl∆curl problems