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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.20408 |
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| _version_ | 1866910006883909632 |
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| author | Chen, Long Huang, Xuehai |
| author_facet | Chen, Long Huang, Xuehai |
| contents | This paper introduces a novel tangential-normal ($t$-$n$) decomposition for finite element differential forms, presenting a new framework for constructing bases in finite element exterior calculus. The main contribution is the development of a $t$-$n$ basis where degrees of freedom and shape functions are explicitly dual, a property that streamlines stiffness matrix assembly and enhances the efficiency of interpolation and numerical integration. Additionally, the integration of the well-documented Lagrange element basis supports practical implementation of finite element differential forms in applications. A geometric decomposition using newly defined bubble polynomial forms is also presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_20408 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tangential-Normal Decompositions of Finite Element Differential Forms Chen, Long Huang, Xuehai Numerical Analysis 58A10, 58J10, 65N30 This paper introduces a novel tangential-normal ($t$-$n$) decomposition for finite element differential forms, presenting a new framework for constructing bases in finite element exterior calculus. The main contribution is the development of a $t$-$n$ basis where degrees of freedom and shape functions are explicitly dual, a property that streamlines stiffness matrix assembly and enhances the efficiency of interpolation and numerical integration. Additionally, the integration of the well-documented Lagrange element basis supports practical implementation of finite element differential forms in applications. A geometric decomposition using newly defined bubble polynomial forms is also presented. |
| title | Tangential-Normal Decompositions of Finite Element Differential Forms |
| topic | Numerical Analysis 58A10, 58J10, 65N30 |
| url | https://arxiv.org/abs/2410.20408 |