A nonlocal coupled system: analysis and discretization
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917442578546688 |
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| author | Bersetche, Francisco Otarola, Enrique Quero, Daniel |
| author_facet | Bersetche, Francisco Otarola, Enrique Quero, Daniel |
| contents | We analyze a nonlocal coupled system arising as the Euler--Lagrange equations of an energy functional involving regional fractional Laplacians of orders $s_1$ and $s_2$ ($ 0 < s_1,s_2 < 1$), each acting on a separate disjoint domain and coupled through a nonlocal interaction term depending on a kernel $J$. Under suitable assumptions on the domains and the kernel, we prove existence and uniqueness of the energy minimizer and derive regularity estimates in fractional Sobolev spaces. We introduce a finite element discretization and establish a priori error estimates. We develop an alternating Schwarz-type method for both the continuous and discrete problems and prove its geometric convergence. Numerical experiments validate the theoretical predictions and illustrate the performance of the method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_25081 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A nonlocal coupled system: analysis and discretization Bersetche, Francisco Otarola, Enrique Quero, Daniel Numerical Analysis We analyze a nonlocal coupled system arising as the Euler--Lagrange equations of an energy functional involving regional fractional Laplacians of orders $s_1$ and $s_2$ ($ 0 < s_1,s_2 < 1$), each acting on a separate disjoint domain and coupled through a nonlocal interaction term depending on a kernel $J$. Under suitable assumptions on the domains and the kernel, we prove existence and uniqueness of the energy minimizer and derive regularity estimates in fractional Sobolev spaces. We introduce a finite element discretization and establish a priori error estimates. We develop an alternating Schwarz-type method for both the continuous and discrete problems and prove its geometric convergence. Numerical experiments validate the theoretical predictions and illustrate the performance of the method. |
| title | A nonlocal coupled system: analysis and discretization |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2604.25081 |