A new div-div-conforming symmetric tensor finite element space with applications to the biharmonic equation

Abstract

A new H ( div ⁡ div ) H(\operatorname {div}\operatorname {div}) -conforming finite element is presented, which avoids the need for supersmoothness 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 C^0 discontinuous Galerkin methods for the biharmonic equation are derived.