Submitted

Finite Element de Rham and Stokes Complexes in Three Dimensions

Long Chen and Xuehai Huang

Submitted

arXiv   Bibtex

ABSTRACT:

Finite element de Rham complexes and finite element Stokes
complexes with various smoothness in three dimensions are
systematically constructed.  First smooth scalar finite elements in
three dimensions are derived through a non-overlapping decomposition
of the simplicial lattice.  Based on the smooth scalar finite
elements, both $H(\div)$-conforming finite elements and
$H(\curl)$-conforming finite elements with various smoothness are
devised, which induce the finite element de Rham complexes with
various smoothness and the associated commutative diagrams. The div
stability is established for the $H(\div)$-conforming finite elements,
and the exactness of these finite element complexes.