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

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS ACS Applied Bio Materials Pub Date : 2024-02-22 DOI:10.1090/mcom/3957

Long Chen, Xuehai Huang

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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.

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一种新的二分对称张量有限元空间及其在双谐波方程中的应用

本文提出了一种新的 H ( div div ) H(\operatorname {div}\operatorname {div}) 顺应有限元，通过将自由度重新分配到边和面，避免了对超平滑性的需求。这就为双谐波方程带来了一种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 复数。最后，推导出了双谐波方程的新弱 Galerkin 方法和 C 0 C^0 非连续 Galerkin 方法。

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