An Immersed $C^0$ Interior Penalty Method for Biharmonic Interface Problems
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916045837565952 |
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| author | Chen, Yuan Zhang, Xu |
| author_facet | Chen, Yuan Zhang, Xu |
| contents | In this paper, we introduce an immersed $C^0$ interior penalty method for solving two-dimensional biharmonic interface problems on unfitted meshes. To accommodate the biharmonic interface conditions, high-order immersed finite element (IFE) spaces are constructed in the least-squares sense. We establish key properties of these spaces including unisolvency and partition of unity are, and verify their optimal approximation capability. These spaces are further incorporated into a modified $C^0$ interior penalty scheme with additional penalty terms on interface segments. The well-posedness of the discrete solution is proved. Numerical experiments with various interface geometries confirm optimal convergence of the proposed method in $L^2$, $H^1$ and $H^2$ norms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_12555 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An Immersed $C^0$ Interior Penalty Method for Biharmonic Interface Problems Chen, Yuan Zhang, Xu Numerical Analysis 35R05, 65N15, 65N30 In this paper, we introduce an immersed $C^0$ interior penalty method for solving two-dimensional biharmonic interface problems on unfitted meshes. To accommodate the biharmonic interface conditions, high-order immersed finite element (IFE) spaces are constructed in the least-squares sense. We establish key properties of these spaces including unisolvency and partition of unity are, and verify their optimal approximation capability. These spaces are further incorporated into a modified $C^0$ interior penalty scheme with additional penalty terms on interface segments. The well-posedness of the discrete solution is proved. Numerical experiments with various interface geometries confirm optimal convergence of the proposed method in $L^2$, $H^1$ and $H^2$ norms. |
| title | An Immersed $C^0$ Interior Penalty Method for Biharmonic Interface Problems |
| topic | Numerical Analysis 35R05, 65N15, 65N30 |
| url | https://arxiv.org/abs/2509.12555 |