Abstract: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.
| Subjects: | Numerical Analysis (math.NA) |
| MSC classes: | 35R05, 65N15, 65N30 |
| Cite as: | arXiv:2509.12555 [math.NA] |
| (or arXiv:2509.12555v2 [math.NA] for this version) | |
| https://doi.org/10.48550/arXiv.2509.12555 arXiv-issued DOI via DataCite |
From: Xu Zhang [view email]
[v1]
Tue, 16 Sep 2025 01:20:56 UTC (1,753 KB)
[v2]
Tue, 26 May 2026 04:56:30 UTC (1,760 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。