Long Chen, Xuehai Huang
Published 2022-06-20Version 1
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.
Comments: 44 pages. arXiv admin note: text overlap with arXiv:2111.10712
Complexes from Complexes: Finite Element Complexes in Three Dimensions
Nonconforming finite element Stokes complexes in three dimensions
Finite elements for divdiv-conforming symmetric tensors in three dimensions
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