Discrete hypocoercivity for a nonlinear kinetic reaction model

2024/03/07 by Marianne Bessemoulin-Chatard, Bessemoulin-Chatard, Marianne, Tino Laidin +3 · 1 voice · 2 citations
Mathematics · #65M08 #65M12 #82B40 #FOS: Mathematics #Numerical Analysis (math.NA) #math.NA

paper · pdf · doi:10.48550/arxiv.2403.04699

Abstract

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 L² 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.

Cited by

• Discrete H-theorem for a finite volume discretization of a nonlinear kinetic system: application to hypocoercivity
• Asymptotic numerical hypocoercivity of the space-time discontinuous Galerkin method for Kolmogorov equation

Discussions

• La première chose à faire est de vérifier si le papier n'a pas été déposé dans une archive ouverte comme HAL ou arXiv. Comme je suis quelqu'un de bien c'est le cas : arxiv.org/abs/2403.04699 [bsky, 1 points, 1 comments]

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