Analysis of Asymptotic Preserving DG-IMEX Schemes for Linear Kinetic Transport Equations in a Diffusive Scaling

In this paper, some theoretical aspects will be addressed for the asymptotic preserving DG-IMEX schemes recently proposed in [10] for kinetic transport equations under a diffusive scaling. We will focus on the methods that are based on discontinuous Galerkin (DG) spatial discretizations with the P k polynomial space and a first order IMEX temporal discretization, and apply them to two linear models: the telegraph equation and the one-group transport equation in slab geometry. In particular, we will establish uniform numerical stability with respect to Knudsen number ε using energy methods, as well as error estimates for any given ε. When ε → 0, a rigorous asymptotic analysis of the schemes is also obtained. Though the methods and the analysis are presented for one dimension in space, they can be generalized to higher dimensions directly.