Conforming finite element DIVDIV complexes and the application for the linearized Einstein-Bianchi system

This paper presents the first family of conforming finite element divdiv complexes on tetrahedral grids in three dimensions. In these complexes, finite element spaces of $H(\text{divdiv},Ω;\mathbb{S})$ are from a current preprint [Chen and Huang, arXiv: 2007.12399, 2020] while finite element spaces of both $H(\text{symcurl},Ω;\mathbb{T})$ and $H^1(Ω;\mathbb{R}^3)$ are newly constructed here. It is proved that these finite element complexes are exact. As a result, they can be used to discretize the linearized Einstein-Bianchi system within the dual formulation.

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