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# 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(divdiv,Ω;𝕊) are from a current preprint [Chen and Huang, arXiv: 2007.12399, 2020] while finite element spaces of both H(symcurl,Ω;𝕋) and H^1(Ω;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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04/17/2022

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