Finite Elements for div- and divdiv-Conforming Symmetric Tensors in Arbitrary Dimension
Finite Elements for div- and divdiv-Conforming Symmetric Tensors in Arbitrary Dimension
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DOI：
10.1137/21m1433708
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发表时间：
2021-06
期刊：
影响因子：
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通讯作者：
Long Chen;Xuehai Huang
中科院分区：
文献类型：
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作者：
Long Chen;Xuehai Huang
本文构造了任意维单形上对称张量的可分形和可分形有限元。首先将形状函数空间分割为迹空间和泡空间。后者进一步分解为微分算子及其正交补的零空间。本文给出了对偶空间的表征，而不是形状函数空间的这些子空间的表征。首先构造了矢量分形有限元作为实例。然后构造新的对称非协调有限元。然后将对偶子空间作为构建块来构造可分的符合有限元。
Several div-conforming and divdiv-conforming finite elements for symmetric tensors on simplexes in arbitrary dimension are constructed in this work. The shape function space is first split as the trace space and the bubble space. The later is further decomposed into the null space of the differential operator and its orthogonal complement. Instead of characterization of these subspaces of the shape function space, characterization of the dual spaces are provided. Vector div-conforming finite elements are firstly constructed as an introductory example. Then new symmetric div-conforming finite elements are constructed. The dual subspaces are then used as build blocks to construct divdiv conforming finite elements.