Continuous Finite Element Method For Maxwell Eigenvalue Problems With Regular Decomposition Technique
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912770896691200 |
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| author | Liao, Feiyi Liu, Haochen Xie, Hehu |
| author_facet | Liao, Feiyi Liu, Haochen Xie, Hehu |
| contents | With the regular decomposition technique, we decompose the space $\mathbf{H}_0^s(\mathbf{curl}; Ω)$ into the sum of a vector potential space and the gradient of a scalar space, both possessing higher regularity. Based on this new high order regular decomposition, a novel numerical method using standard high order Lagrange finite elements is designed for solving Maxwell eigenvalue problems. Specifically, the full convergence orders of the eigenpair approximations are proved for the proposed numerical method. Finally, numerical examples are provided to validate the proposed scheme and confirm the theoretical convergence results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_15314 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Continuous Finite Element Method For Maxwell Eigenvalue Problems With Regular Decomposition Technique Liao, Feiyi Liu, Haochen Xie, Hehu Numerical Analysis 65N30, 65N25, 65L15, 65B99 With the regular decomposition technique, we decompose the space $\mathbf{H}_0^s(\mathbf{curl}; Ω)$ into the sum of a vector potential space and the gradient of a scalar space, both possessing higher regularity. Based on this new high order regular decomposition, a novel numerical method using standard high order Lagrange finite elements is designed for solving Maxwell eigenvalue problems. Specifically, the full convergence orders of the eigenpair approximations are proved for the proposed numerical method. Finally, numerical examples are provided to validate the proposed scheme and confirm the theoretical convergence results. |
| title | Continuous Finite Element Method For Maxwell Eigenvalue Problems With Regular Decomposition Technique |
| topic | Numerical Analysis 65N30, 65N25, 65L15, 65B99 |
| url | https://arxiv.org/abs/2512.15314 |