Submitted

Complexes from Complexes: Finite Element Complexes in Three Dimensions

Long Chen and Xuehai Huang

Submitted

arXiv   Bibtex

ABSTRACT:

 Finite element Hessian, elasticity, and divdiv complexes are
systematically derived via Bernstein-Gelfand-Gelfand (BGG) framework
developed by Arnold and Hu [Complexes from
complexes. Found. Comput. Math., 2021]. Our construction is built on
three major tools: smooth finite element de Rham complexes, the t−n
decomposition approach for constructing div-conforming elements, and
the trace complexes and corresponding 2D finite element complexes. Two
reduction operators are introduced to solve the mis-match of
continuity of the BGG diagram in the continuous level.