A seamless local-nonlocal coupling diffusion model with $H^1$ vanishing nonlocality convergence
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911017644064768 |
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| author | Meng, Yanzun Shi, Zuoqiang |
| author_facet | Meng, Yanzun Shi, Zuoqiang |
| contents | Based on the development in dealing with nonlocal boundary conditions, we propose a seamless local-nonlocal coupling diffusion model in this paper. In our model, a finite constant interaction horizon is equipped in the nonlocal part and transmission conditions are imposed on a co-dimension one interface. To achieve a seamless coupling, we introduce an auxiliary function to merge the nonlocal model with the local part and design a proper coupling transmission condition to ensure the stability and convergence. In addition, by introducing bilinear form, well-posedness of the proposed model can be proved and convergence to a standard elliptic transmission model with first order in $H^1$ norm can be derived. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_03153 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A seamless local-nonlocal coupling diffusion model with $H^1$ vanishing nonlocality convergence Meng, Yanzun Shi, Zuoqiang Analysis of PDEs Based on the development in dealing with nonlocal boundary conditions, we propose a seamless local-nonlocal coupling diffusion model in this paper. In our model, a finite constant interaction horizon is equipped in the nonlocal part and transmission conditions are imposed on a co-dimension one interface. To achieve a seamless coupling, we introduce an auxiliary function to merge the nonlocal model with the local part and design a proper coupling transmission condition to ensure the stability and convergence. In addition, by introducing bilinear form, well-posedness of the proposed model can be proved and convergence to a standard elliptic transmission model with first order in $H^1$ norm can be derived. |
| title | A seamless local-nonlocal coupling diffusion model with $H^1$ vanishing nonlocality convergence |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2412.03153 |