# Diffusion limit

## An Asymptotic Preserving scheme for the diffusion limit of a stochastic linear kinetic equation

In this paper, we present an Asymptotic Preserving scheme for a stochastic linear kinetic equation. Its construction is based on a micro-macro decomposition. We start by explaining how we build it and then perform the formal numerical limit. After …

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

We present an asymptotic preserving scheme based on a micro-macro decomposition for stochastic linear transport equations in kinetic and diffusive regimes. We perfom a mathemat- ical analysis and prove that the scheme is uniformly stable with respect …

## Regularity of velocity averages for transport equations on random discrete velocity grids

We go back to the question of the regularity of the velocity average ${\int f(x,v)\psi(v) d \mu( v)}$when $f$ and $v\cdot \nabla\_xf$ both belong to $L^2$, and the variable $v$ lies in a discrete subset of $\mathbb R^D$. First of all, we provide a …

## Stochastic Discrete Velocity Averaging Lemmas and Rosseland Approximation

In this note, we investigate some questions around velocity averaging lemmas, a class of results which ensure the regularity of the velocity average ${\int f(x,v)\psi(v) d \mu( v)}$ when $v\cdot \nabla\_xf$ both belong to $L^p$, $p \in \[1, \infty)$ …

## Influence du stochastique sur des problèmatiques de changement d'échelle

The work of this thesis belongs to the field of partial differential equations. More specifically, it is linked to the problematic of scale changes in the context of kinetic of gas. Indeed, knowing that there exists different scales of description for a gas (microscopic, mesoscopic and macroscopic scale), we want to link these different associated scales in a context where some randomness acts, in initial data and/or distributed on all the time interval.