  Finite element de Rham complexes and finite element Stokes complexes with
various smoothness in three dimensions are systematically constructed. First
smooth scalar finite elements in three dimensions are derived through a
non-overlapping decomposition of the simplicial lattice. Based on the smooth
scalar finite elements, both H(div)-conforming finite elements and
H(curl)-conforming finite elements with various smoothness are devised, which
induce the finite element de Rham complexes with various smoothness and the
associated commutative diagrams. The div stability is established for the
H(div)-conforming finite elements, and the exactness of these finite element
complexes.

Numerical Analysis;Numerical Analysis