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

Long Chen; Xuehai Huang

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

Numerical Analysis 2024-03-18 v4 Numerical Analysis

Authors: Long Chen , Xuehai Huang

Abstract

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.

Keywords

divdiv-conforming finite element biharmonic equation hybridizable mixed method superconvergence finite element complex weak galerkin method discontinuous galerkin method

Cite

@article{arxiv.2305.11356,
  title  = {A New Div-Div-Conforming Symmetric Tensor Finite Element Space with Applications to the Biharmonic Equation},
  author = {Long Chen and Xuehai Huang},
  journal= {arXiv preprint arXiv:2305.11356},
  year   = {2024}
}

Comments

38 pages, 2 figures

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