Published

Finite elements for div and divdiv conforming symmetric tensors in arbitrary dimensions

Long Chen and Xuehai Huang

SIAM Journal on Numerical Analysis, 60: 1932--1961, 2022.

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ABSTRACT:

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 characterizations of these subspaces of the
shape function space, characterizations of corresponding degrees of
freedom in 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 new divdiv
conforming finite elements.