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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2509.18348 |
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| _version_ | 1866915507008962560 |
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| author | Borthagaray, Juan Pablo de León, Nahuel |
| author_facet | Borthagaray, Juan Pablo de León, Nahuel |
| contents | The mixed formulation of the classical Poisson problem introduces the flux as an additional variable, leading to a system of coupled equations. Using fractional calculus identities, in this work we explore a mixed formulation of the fractional Poisson problem and establish its well-posedness. Since a direct discretization of this problem appears to be out of reach, we adapt a stabilized approach by Hughes and Masud, which yields a coercive and well-posed formulation. The coercivity ensures the stability of any conforming finite element discretization. We further prove the convergence of this discretization, derive convergence rates, and discuss implementation aspects. Finally, we present numerical experiments that highlight both the importance of stabilization and the accuracy of our theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_18348 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A mixed formulation for the fractional Poisson problem Borthagaray, Juan Pablo de León, Nahuel Numerical Analysis Analysis of PDEs The mixed formulation of the classical Poisson problem introduces the flux as an additional variable, leading to a system of coupled equations. Using fractional calculus identities, in this work we explore a mixed formulation of the fractional Poisson problem and establish its well-posedness. Since a direct discretization of this problem appears to be out of reach, we adapt a stabilized approach by Hughes and Masud, which yields a coercive and well-posed formulation. The coercivity ensures the stability of any conforming finite element discretization. We further prove the convergence of this discretization, derive convergence rates, and discuss implementation aspects. Finally, we present numerical experiments that highlight both the importance of stabilization and the accuracy of our theoretical results. |
| title | A mixed formulation for the fractional Poisson problem |
| topic | Numerical Analysis Analysis of PDEs |
| url | https://arxiv.org/abs/2509.18348 |