Before revision:  Hilbert complex and polynomial complexes are presented and several decomposition of polynomial vector and tensors spaces are revealed from the complexes . The constructed divdiv conforming elements are exploited to discretize the mixed formulation of the biharmonic equation. Optimal order and superconvergence error analysis is provided. Hybridization is given for the ease of implementation .
After revision:  Hilbert complex and polynomial complexes are presented and several decomposition of polynomial vector and tensors spaces are revealed from the complexes .