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arXiv · 2008.03793

A family of finite element Stokes complexes in three dimensions

Kaibo Hu·Qian Zhang·Zhimin Zhang
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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.

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Kaibo Hu, Qian Zhang, Zhimin Zhang. 2021-10-31. A family of finite element Stokes complexes in three dimensions. https://arxiv.org/abs/2008.03793

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