A deterministic particle method for the porous media equation
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866913671799635968 |
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| author | Amassad, Amina Zhou, Datong |
| author_facet | Amassad, Amina Zhou, Datong |
| contents | This paper deals with the deterministic particle method for the equation of porous media (with p = 2). We establish a convergence rate in the Wasserstein-2 distance between the approximate solution of the associated nonlinear transport equation and the solution of the original one. This seems to be the first quantitative rate for diffusion-velocity particle methods solving diffusive equations and is achieved using a novel commutator estimate for the Wasserstein transport map. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_18745 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A deterministic particle method for the porous media equation Amassad, Amina Zhou, Datong Analysis of PDEs Numerical Analysis Mathematical Physics This paper deals with the deterministic particle method for the equation of porous media (with p = 2). We establish a convergence rate in the Wasserstein-2 distance between the approximate solution of the associated nonlinear transport equation and the solution of the original one. This seems to be the first quantitative rate for diffusion-velocity particle methods solving diffusive equations and is achieved using a novel commutator estimate for the Wasserstein transport map. |
| title | A deterministic particle method for the porous media equation |
| topic | Analysis of PDEs Numerical Analysis Mathematical Physics |
| url | https://arxiv.org/abs/2501.18745 |