Shi Jin University of Wisconsin-MadisonJian-Guo LiuDuke UniversityZheng MaShanghai Jiao Tong Unviersity
Numerical Analysis and Scientific Computingmathscidoc:1702.25019
In this paper we study the stochastic Galerkin approximation for the linear transport equation with random inputs and diffusive scal- ing. We first establish uniform (in the Knudsen number) stability results in the random space for the transport equation with uncertain scattering coefficients, and then prove the uniform spectral conver- gence (and consequently the sharp stochastic Asymptotic-Preserving property) of the stochastic Galerkin method. A micro-macro decom- position based fully discrete scheme is adopted for the problem and proved to have a uniform stability. Numerical experiments are conducted to demonstrate the stability and asymptotic properties of the method.
linear transport equation, random inputs, diffusion limit, uncertainty quanti