Interior penalty DG methods for Maxwell's equations in dispersive media

摘要

In this paper, we develop a fully-discrete interior penalty discontinuous Galerkin method for solving the time-dependent Maxwell's equations in dispersive media. The model is described by a vector integral-differential equation. Our scheme is proved to be unconditionally stable and achieve optimal error estimates in both L~2 norm and energy norm. The scheme is implemented and numerical results supporting our analysis are presented.