A Nonconforming Finite Element Method for Elliptic Interface Problems on Locally Anisotropic Meshes
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911194506330112 |
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| author | Geng, Chenchen Wang, Hua Zhang, Qichen |
| author_facet | Geng, Chenchen Wang, Hua Zhang, Qichen |
| contents | We propose a new nonconforming \(P_1\) finite element method for elliptic interface problems. The method is constructed on a locally anisotropic mixed mesh, which is generated by fitting the interface through a simple connection of intersection points on an interface-unfitted background mesh, as introduced in \cite{Hu2021optimal}. We first establish interpolation error estimates on quadrilateral elements satisfying the regular decomposition property (RDP). Building on this, the main contribution of this work is a novel consistency error analysis for nonconforming elements, which removes the quasi-regularity assumption commonly required in existing approaches. Numerical results confirm the theoretical convergence rates and demonstrate the robustness and accuracy of the proposed method. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_15077 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Nonconforming Finite Element Method for Elliptic Interface Problems on Locally Anisotropic Meshes Geng, Chenchen Wang, Hua Zhang, Qichen Numerical Analysis We propose a new nonconforming \(P_1\) finite element method for elliptic interface problems. The method is constructed on a locally anisotropic mixed mesh, which is generated by fitting the interface through a simple connection of intersection points on an interface-unfitted background mesh, as introduced in \cite{Hu2021optimal}. We first establish interpolation error estimates on quadrilateral elements satisfying the regular decomposition property (RDP). Building on this, the main contribution of this work is a novel consistency error analysis for nonconforming elements, which removes the quasi-regularity assumption commonly required in existing approaches. Numerical results confirm the theoretical convergence rates and demonstrate the robustness and accuracy of the proposed method. |
| title | A Nonconforming Finite Element Method for Elliptic Interface Problems on Locally Anisotropic Meshes |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2506.15077 |