Geometric Decomposition and Efficient Implementation of High Order Face and Edge Elements
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913344384925696 |
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| author | Chen, Chunyu Chen, Long Huang, Xuehai Wei, Huayi |
| author_facet | Chen, Chunyu Chen, Long Huang, Xuehai Wei, Huayi |
| contents | This study investigates high-order face and edge elements in finite element methods, with a focus on their geometric attributes, indexing management, and practical application. The exposition begins by a geometric decomposition of Lagrange finite elements, setting the foundation for further analysis. The discussion then extends to $H(\rm{div})$-conforming and $H(\rm{curl})$-conforming finite element spaces, adopting variable frames across differing sub-simplices. The imposition of tangential or normal continuity is achieved through the strategic selection of corresponding bases. The paper concludes with a focus on efficient indexing management strategies for degrees of freedom, offering practical guidance to researchers and engineers. It serves as a comprehensive resource that bridges the gap between theory and practice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_13843 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Geometric Decomposition and Efficient Implementation of High Order Face and Edge Elements Chen, Chunyu Chen, Long Huang, Xuehai Wei, Huayi Numerical Analysis 65N30, 35Q60 This study investigates high-order face and edge elements in finite element methods, with a focus on their geometric attributes, indexing management, and practical application. The exposition begins by a geometric decomposition of Lagrange finite elements, setting the foundation for further analysis. The discussion then extends to $H(\rm{div})$-conforming and $H(\rm{curl})$-conforming finite element spaces, adopting variable frames across differing sub-simplices. The imposition of tangential or normal continuity is achieved through the strategic selection of corresponding bases. The paper concludes with a focus on efficient indexing management strategies for degrees of freedom, offering practical guidance to researchers and engineers. It serves as a comprehensive resource that bridges the gap between theory and practice. |
| title | Geometric Decomposition and Efficient Implementation of High Order Face and Edge Elements |
| topic | Numerical Analysis 65N30, 35Q60 |
| url | https://arxiv.org/abs/2309.13843 |