Discrete hypocoercivity for a nonlinear kinetic reaction model
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866914707586154496 |
|---|---|
| author | Bessemoulin-Chatard, Marianne Laidin, Tino Rey, Thomas |
| author_facet | Bessemoulin-Chatard, Marianne Laidin, Tino Rey, Thomas |
| contents | In this article, we propose a finite volume discretization of a one dimensional nonlinear reaction kinetic model proposed in [Neumann, Schmeiser, Kint. Rel. Mod. 2016], which describes a 2-species recombination-generation process. Specifically, we establish the long-time convergence of approximate solutions towards equilibrium, at exponential rate. The study is based on an adaptation for a discretization of the linearized problem of the $L^2$ hypocoercivity method introduced in [Dolbeault, Mouhot, Schmeiser, 2015]. From this, we can deduce a local result for the discrete nonlinear problem. As in the continuous framework, this result requires the establishment of a maximum principle, which necessitates the use of monotone numerical fluxes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_04699 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Discrete hypocoercivity for a nonlinear kinetic reaction model Bessemoulin-Chatard, Marianne Laidin, Tino Rey, Thomas Numerical Analysis 82B40, 65M08, 65M12 In this article, we propose a finite volume discretization of a one dimensional nonlinear reaction kinetic model proposed in [Neumann, Schmeiser, Kint. Rel. Mod. 2016], which describes a 2-species recombination-generation process. Specifically, we establish the long-time convergence of approximate solutions towards equilibrium, at exponential rate. The study is based on an adaptation for a discretization of the linearized problem of the $L^2$ hypocoercivity method introduced in [Dolbeault, Mouhot, Schmeiser, 2015]. From this, we can deduce a local result for the discrete nonlinear problem. As in the continuous framework, this result requires the establishment of a maximum principle, which necessitates the use of monotone numerical fluxes. |
| title | Discrete hypocoercivity for a nonlinear kinetic reaction model |
| topic | Numerical Analysis 82B40, 65M08, 65M12 |
| url | https://arxiv.org/abs/2403.04699 |