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

Long Chen; Xuehai Huang

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arXiv · 2305.11356

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

Long Chen·Xuehai Huang

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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.

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Long Chen, Xuehai Huang. 2024-03-15. A New Div-Div-Conforming Symmetric Tensor Finite Element Space with Applications to the Biharmonic Equation. https://arxiv.org/abs/2305.11356

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