Error analysis of a discontinuous Galerkin method for Maxwell equations in dispersive media

A discontinuous Galerkin method for the numerical approximation of time-dependent Maxwell equations in three different dispersive media is introduced. Both the L2-stability and error estimate of the DG method are discussed in detail. We show that the proposed method has an accuracy of O ( h k + 1 2 ) under the L2-norm when polynomials of degree k in space are used. Furthermore, numerical experiments are provided to justify our theoretical analysis.