Abstract
In this paper, we consider the linear transport equation under diffusive scaling and with random inputs. The method is based on the generalized polynomial chaos approach in the stochastic Galerkin framework. Several theoretical aspects will be addressed. A uniform numerical stability with respect to the Knudsen number , and a uniform in error estimate is given. For temporal and spatial discretizations, we apply the implicit-explicit scheme under the micro-macro decomposition framework and the discontinuous Galerkin method, as proposed in Jang et al. (SIAM J Numer Anal 52:2048-2072, 2014) for deterministic problem. We provide a rigorous proof of the stochastic asymptotic-preserving (sAP) property. Extensive numerical experiments that validate the accuracy and sAP of the method are conducted.