Monotone two-scale methods for a class of integrodifferential operators and applications
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866914889400844288 |
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| author | Borthagaray, Juan Pablo Nochetto, Ricardo H. Salgado, Abner J. Torres, Céline |
| author_facet | Borthagaray, Juan Pablo Nochetto, Ricardo H. Salgado, Abner J. Torres, Céline |
| contents | We develop a monotone, two-scale discretization for a class of integrodifferential operators of order $2s$, $s \in (0,1)$. We apply it to develop numerical schemes, and derive pointwise convergence rates, for linear and obstacle problems governed by such operators. As applications of the monotonicity, we provide error estimates for free boundaries and a convergent numerical scheme for a concave fully nonlinear, nonlocal, problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_17652 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Monotone two-scale methods for a class of integrodifferential operators and applications Borthagaray, Juan Pablo Nochetto, Ricardo H. Salgado, Abner J. Torres, Céline Numerical Analysis We develop a monotone, two-scale discretization for a class of integrodifferential operators of order $2s$, $s \in (0,1)$. We apply it to develop numerical schemes, and derive pointwise convergence rates, for linear and obstacle problems governed by such operators. As applications of the monotonicity, we provide error estimates for free boundaries and a convergent numerical scheme for a concave fully nonlinear, nonlocal, problem. |
| title | Monotone two-scale methods for a class of integrodifferential operators and applications |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2405.17652 |