CONFORMING FINITE ELEMENT DIVDIV COMPLEXES AND THE APPLICATION FOR THE LINEARIZED EINSTEIN-BIANCHI SYSTEM

This paper presents the first family of conforming finite element div div complexes on tetrahedral grids in three dimensions. In these complexes, finite element spaces of H(div div, Ω; S) are from a recent article [L. Chen and X. Huang, Math. Comp., 91 (2022), pp. 1107-1142] while finite element spaces of both H(sym curl, Ω; T) and H¹(Ω; ℝ³) 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.