FINITE ELEMENTS FOR DIV- AND DIVDIV-CONFORMING SYMMETRIC TENSORS IN ARBITRARY DIMENSION

作者：Chen, Long; Huang, Xuehai^*

来源：SIAM Journal on Numerical Analysis, 2022, 60(4): 1932-1961.

DOI：10.1137/21M1433708

• symmetric tensor
• div-conforming finite elements
• divdiv-conforming finite ele-ments
• space decomposition
• dual approach

Several div-conforming and divdiv-conforming finite elements for symmetric ten-sors 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 characterizations of these subspaces of the shape function space, characterizations of corresponding degrees of free-dom in the dual spaces are provided. Vector div-conforming finite elements are first constructed as an introductory example. Then new symmetric div-conforming finite elements are construc-ted. The dual subspaces are then used as build blocks to construct new divdiv-conforming finite elements.