Decoupled finite element methods for a fourth-order exterior differential equation
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910835287261184 |
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| author | Cui, Xuewei Huang, Xuehai |
| author_facet | Cui, Xuewei Huang, Xuehai |
| contents | This paper proposes novel decoupled finite element methods for a fourth-order exterior differential equation. Based on differential complexes and the Helmholtz decomposition, the fourth-order exterior differential equation is decomposed into two second-order exterior differential equations and one generalized Stokes equation. A key advantage of this decoupled formulation is that it avoids the use of quotient spaces. A family of conforming finite element methods are developed for the decoupled formulation. Numerical results are provided for verifying the decoupled finite element methods of the biharmonic equation in three dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_09689 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Decoupled finite element methods for a fourth-order exterior differential equation Cui, Xuewei Huang, Xuehai Numerical Analysis 58J10, 65N30, 65N12, 65N22 This paper proposes novel decoupled finite element methods for a fourth-order exterior differential equation. Based on differential complexes and the Helmholtz decomposition, the fourth-order exterior differential equation is decomposed into two second-order exterior differential equations and one generalized Stokes equation. A key advantage of this decoupled formulation is that it avoids the use of quotient spaces. A family of conforming finite element methods are developed for the decoupled formulation. Numerical results are provided for verifying the decoupled finite element methods of the biharmonic equation in three dimensions. |
| title | Decoupled finite element methods for a fourth-order exterior differential equation |
| topic | Numerical Analysis 58J10, 65N30, 65N12, 65N22 |
| url | https://arxiv.org/abs/2410.09689 |