A family of conforming finite element divdiv complexes on cuboid meshes

In this paper, the first family of conforming finite element divdiv complexes on cuboid meshes is constructed. The complex exhibits exactness on a contractible domain in the sense that the kernel space of each successive discrete map is the range of the previous one. This allows for algebraic structure-preserving finite element discretization of both the biharmonic equation and the linearized Einstein–Bianchi system. The convergence of optimal order is established and validated through numerical examples.