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03 November 2024 |
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Article overview
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Finite Element Complexes in Two Dimensions | Long Chen
; Xuehai Huang
; | Date: |
2 Jun 2022 | Abstract: | Two-dimensional finite element complexes with various smoothness, including
the de Rham complex, the curldiv complex, the elasticity complex, and the
divdiv complex, are systematically constructed in this work. First smooth
scalar finite elements in two dimensions are developed based on a
non-overlapping decomposition of the simplicial lattice and the Bernstein basis
of the polynomial space. Smoothness at vertices is more than doubled than that
at edges. Then the finite element de Rham complexes with various smoothness are
devised using smooth finite elements with smoothness parameters satisfying
certain relations. Finally, finite element elasticity complexes and finite
element divdiv complexes are derived from finite element de Rham complexes by
using the Bernstein-Gelfand-Gelfand (BGG) framework. Additionally, some finite
element divdiv complexes are constructed without BGG framework. Dimension count
plays an important role for verifying the exactness of two-dimensional finite
element complexes. | Source: | arXiv, 2206.00851 | Services: | Forum | Review | PDF | Favorites |
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