Complexes from Complexes: Finite Element Complexes in Three Dimensions

Long Chen, Xuehai Huang

Published 2022-11-16Version 1

Finite element Hessian, elasticity, and divdiv complexes are systematically derived via Bernstein-Gelfand-Gelfand (BGG) framework developed by Arnold and Hu [Complexes from complexes. {\em 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.