Analysis of an asymptotic preserving scheme for stochastic linear\n kinetic equations in the diffusion limit

2018/03/16 by Nathalie Ayi, Erwan Faou, Ayi, Nathalie +1 · 1 citation
Economics, Econometrics and Finance · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Markov Chains and Monte Carlo Methods #Numerical Analysis (math.NA) #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1803.06130

openalex publication_date 2018/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present an asymptotic preserving scheme based on a micro-macro\ndecomposition for stochastic linear transport equations in kinetic and\ndiffusive regimes. We perfom a mathematical analysis and prove that the scheme\nis uniformly stable with respect to the mean free path of the particles in the\nsimple telegraph model and in the general case. We present several numerical\ntests which validate our scheme.\n

Cited by

• Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations

Related

• Analysis of an asymptotic preserving scheme for linear kinetic equations in the diffusion limit
• A Positive Asymptotic Preserving Scheme for Linear Kinetic Transport Equations
• High order asymptotic preserving scheme for linear kinetic equations with diffusive scaling
• Well-balanced and asymptotic preserving schemes for kinetic models
• Some examples of kinetic scheme whose diffusion limit is Il'in's exponential-fitting