Uniformly $hp$-stable elements for the elasticity complex
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866917787383889920 |
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| author | Aznaran, Francis R. A. Hu, Kaibo Parker, Charles |
| author_facet | Aznaran, Francis R. A. Hu, Kaibo Parker, Charles |
| contents | For the discretization of symmetric, divergence-conforming stress tensors in continuum mechanics, we prove inf-sup stability bounds which are uniform in polynomial degree and mesh size for the Hu--Zhang finite element in two dimensions. This is achieved via an explicit construction of a bounded right inverse of the divergence operator, with the crucial component being the construction of bounded Poincaré operators for the stress elasticity complex which are polynomial-preserving, in the Bernstein--Gelfand--Gelfand framework of the finite element exterior calculus. We also construct $hp$-bounded projection operators satisfying a commuting diagram property and $hp$-stable Hodge decompositions. Numerical examples are provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_17414 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uniformly $hp$-stable elements for the elasticity complex Aznaran, Francis R. A. Hu, Kaibo Parker, Charles Numerical Analysis 65N30, 74B05, 74G15, 74S05 For the discretization of symmetric, divergence-conforming stress tensors in continuum mechanics, we prove inf-sup stability bounds which are uniform in polynomial degree and mesh size for the Hu--Zhang finite element in two dimensions. This is achieved via an explicit construction of a bounded right inverse of the divergence operator, with the crucial component being the construction of bounded Poincaré operators for the stress elasticity complex which are polynomial-preserving, in the Bernstein--Gelfand--Gelfand framework of the finite element exterior calculus. We also construct $hp$-bounded projection operators satisfying a commuting diagram property and $hp$-stable Hodge decompositions. Numerical examples are provided. |
| title | Uniformly $hp$-stable elements for the elasticity complex |
| topic | Numerical Analysis 65N30, 74B05, 74G15, 74S05 |
| url | https://arxiv.org/abs/2409.17414 |