A new $H(\textrm{divdiv})$-conforming finite element is presented, which avoids the need for super-smoothness by redistributing the degrees of freedom to edges and faces. This leads to a hybridizable mixed method with superconvergence for the biharmonic equation. Moreover, new finite element divdiv complexes are established. Finally, new weak Galerkin and $C^0$ discontinuous Galerkin methods for the biharmonic equation are derived.

翻译：本文提出了一种新的 $H(\textrm{divdiv})$-协调有限元，通过将自由度重新分配到边和面上，避免了超光滑性的需求。这导致了一种针对双调和方程具有超收敛性的可混合混合方法。此外，还建立了新的有限元 divdiv 复形。最后，推导出了用于双调和方程的新弱 Galerkin 和 $C^0$ 间断 Galerkin 方法。