New low-order mixed finite element methods for linear elasticity
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866916132729913344 |
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| author | Huang, Xuehai Zhang, Chao Zhou, Yaqian Zhu, Yangxing |
| author_facet | Huang, Xuehai Zhang, Chao Zhou, Yaqian Zhu, Yangxing |
| contents | New low-order $H(\textrm{div})$-conforming finite elements for symmetric tensors are constructed in arbitrary dimension. The space of shape functions is defined by enriching the symmetric quadratic polynomial space with the $(d+1)$-order normal-normal face bubble space. The reduced counterpart has only $d(d+1)^2$ degrees of freedom. Basis functions are explicitly given in terms of barycentric coordinates. Low-order conforming finite element elasticity complexes starting from the Bell element, are developed in two dimensions. These finite elements for symmetric tensors are applied to devise robust mixed finite element methods for the linear elasticity problem, which possess the uniform error estimates with respect to the Lamé coefficient $λ$, and superconvergence for the displacement. Numerical results are provided to verify the theoretical convergence rates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_13920 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | New low-order mixed finite element methods for linear elasticity Huang, Xuehai Zhang, Chao Zhou, Yaqian Zhu, Yangxing Numerical Analysis 58J10, 65N12, 65N22, 65N30 New low-order $H(\textrm{div})$-conforming finite elements for symmetric tensors are constructed in arbitrary dimension. The space of shape functions is defined by enriching the symmetric quadratic polynomial space with the $(d+1)$-order normal-normal face bubble space. The reduced counterpart has only $d(d+1)^2$ degrees of freedom. Basis functions are explicitly given in terms of barycentric coordinates. Low-order conforming finite element elasticity complexes starting from the Bell element, are developed in two dimensions. These finite elements for symmetric tensors are applied to devise robust mixed finite element methods for the linear elasticity problem, which possess the uniform error estimates with respect to the Lamé coefficient $λ$, and superconvergence for the displacement. Numerical results are provided to verify the theoretical convergence rates. |
| title | New low-order mixed finite element methods for linear elasticity |
| topic | Numerical Analysis 58J10, 65N12, 65N22, 65N30 |
| url | https://arxiv.org/abs/2310.13920 |