A structure-preserving local discontinuous Galerkin method for the Fokker-Planck-Landau equation
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910966586802176 |
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| author | Huang, Kun Galindo-Olarte, Andrés González-Hernández, Rodrigo Gamba, Irene M. |
| author_facet | Huang, Kun Galindo-Olarte, Andrés González-Hernández, Rodrigo Gamba, Irene M. |
| contents | In this work, we introduce a structure-preserving local discontinuous Galerkin (LDG) method \cite{cockburn1998local} for solving the non-local non-linear Fokker-Planck-Landau (FPL) equations. We rephrase the structure-preserving strategy of Shiroto and Sentoku\cite{shiroto2019structure} in the language of numerical analysis, and extend it to the LDG framework. We propose a method that is not only conservative, but also stabilized through upwind flux. The apparent contradiction between conservation laws and numerical stabilization is elegantly resolved by leveraging the properties of the jump terms inherent to the LDG framework. In the numerical experiments, our scheme is tested with benchmark examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_18321 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A structure-preserving local discontinuous Galerkin method for the Fokker-Planck-Landau equation Huang, Kun Galindo-Olarte, Andrés González-Hernández, Rodrigo Gamba, Irene M. Numerical Analysis In this work, we introduce a structure-preserving local discontinuous Galerkin (LDG) method \cite{cockburn1998local} for solving the non-local non-linear Fokker-Planck-Landau (FPL) equations. We rephrase the structure-preserving strategy of Shiroto and Sentoku\cite{shiroto2019structure} in the language of numerical analysis, and extend it to the LDG framework. We propose a method that is not only conservative, but also stabilized through upwind flux. The apparent contradiction between conservation laws and numerical stabilization is elegantly resolved by leveraging the properties of the jump terms inherent to the LDG framework. In the numerical experiments, our scheme is tested with benchmark examples. |
| title | A structure-preserving local discontinuous Galerkin method for the Fokker-Planck-Landau equation |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2505.18321 |