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Finite element de Rham complexes and finite element Stokes complexes with varying degrees of smoothness in three dimensions are systematically constructed in this paper. Smooth scalar finite elements in three dimensions are derived through a non-overlapping decomposition of the simplicial lattice. H(div)-conforming finite elements and H(curl)-conforming finite elements with varying degrees of smoothness are devised based on these smooth scalar finite elements. The finite element de Rham complexes with corresponding smoothness and commutative diagrams are induced by these elements. The div stability of the H(div)-conforming finite elements is established, and the exactness of these finite element complexes is proven.
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This content will become publicly available on June 30, 2026
Distributional Finite Element curl div Complexes and Application to Quad Curl Problems
This paper addresses the challenge of constructing finite element curl div complexes in three dimensions. Tangential-normal continuity is introduced in order to develop distributional finite element curl div complexes. The spaces constructed are applied to discretize the quad curl problem, demonstrating optimal order of convergence. Furthermore, a hybridization technique is proposed, demonstrating its equivalence to nonconforming finite elements and weak Galerkin methods.
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- PAR ID:
- 10594594
- Publisher / Repository:
- SIAM
- Date Published:
- Journal Name:
- SIAM Journal on Numerical Analysis
- Volume:
- 63
- Issue:
- 3
- ISSN:
- 0036-1429
- Page Range / eLocation ID:
- 1078 to 1104
- Subject(s) / Keyword(s):
- distributional curl div finite element complex quad curl problem error analysis hybridization
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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