Published

A New Div-Div-Conforming Symmetric Tensor Finite Element Space with Applications to the Biharmonic Equation

Long Chen and Xuehai Huang

Mathematics of Computation, March 20, 2024.

arXiv   Bibtex   doi: https://doi.org/10.1090/mcom/3957

ABSTRACT:

 A new $H(\div\div)$-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.