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 …
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 …
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 …
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)$ …