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In this paper, the first family of conforming finite element divdiv complexes on cuboid grids in three dimensions is constructed. Besides, a new family of conforming finite element divdiv complexes with enhanced smoothness on tetrahedral grids is presented. These complexes are exact in the sense that the range of each discrete map is the kernel space of the succeeding one.arXiv:2204.07895v1 fatcat:kxbzqpf4qzhovm3we4hzvh7ooq