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

by   Jun Hu, et al.

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,Ξ©;π•Š) are from a current preprint [Chen and Huang, arXiv: 2007.12399, 2020] while finite element spaces of both H(symcurl,Ξ©;𝕋) and H^1(Ξ©;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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