An asymptotically compatible unfitted finite element methods for nonlocal elliptic Interfaces: local limits and sharp error estimates
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914213806473216 |
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| author | Dong, Haixia Xie, Ziqing Zhang, Jiwei |
| author_facet | Dong, Haixia Xie, Ziqing Zhang, Jiwei |
| contents | This paper presents the development and analysis of an asymptotically compatible (AC) unfitted finite element method for one-dimensional nonlocal elliptic interface problems. The proposed method achieves optimal error estimates through three principal contributions: (i) an extended maximum principle, coupled with an asymptotic consistency analysis of the flux operator, which establishes second-order convergence of nonlocal solutions to their local counterparts in the maximum norm; (ii) a Nitsche-type formulation that directly incorporates nonlocal jump conditions into the weak form, enabling high accuracy without body-fitted meshes; and (iii) a rigorous proof of optimal convergence rates in both the energy and L2 norms via the nonlocal maximum principle, flux consistency, and a newly derived nonlocal Poincare inequality. Numerical experiments confirm the theoretical findings and demonstrate the robustness and efficiency of the proposed approach, thereby providing a foundation for extensions to higher dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_18939 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An asymptotically compatible unfitted finite element methods for nonlocal elliptic Interfaces: local limits and sharp error estimates Dong, Haixia Xie, Ziqing Zhang, Jiwei Numerical Analysis This paper presents the development and analysis of an asymptotically compatible (AC) unfitted finite element method for one-dimensional nonlocal elliptic interface problems. The proposed method achieves optimal error estimates through three principal contributions: (i) an extended maximum principle, coupled with an asymptotic consistency analysis of the flux operator, which establishes second-order convergence of nonlocal solutions to their local counterparts in the maximum norm; (ii) a Nitsche-type formulation that directly incorporates nonlocal jump conditions into the weak form, enabling high accuracy without body-fitted meshes; and (iii) a rigorous proof of optimal convergence rates in both the energy and L2 norms via the nonlocal maximum principle, flux consistency, and a newly derived nonlocal Poincare inequality. Numerical experiments confirm the theoretical findings and demonstrate the robustness and efficiency of the proposed approach, thereby providing a foundation for extensions to higher dimensions. |
| title | An asymptotically compatible unfitted finite element methods for nonlocal elliptic Interfaces: local limits and sharp error estimates |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2512.18939 |