Error analysis of DGTD for linear Maxwell equations with inhomogeneous interface conditions

In the present paper we consider linear and isotropic Maxwell equations with inhomogeneous interface conditions. We discretize the problem with the discontinuous Galerkin method in space and with the leapfrog scheme in time. An analytical setting is provided in which we show well-posedness of the problem, derive stability estimates, and exploit this in the error analysis to prove rigorous error bounds for both the spatial and full discretization. The theoretical findings are confirmed with numerical experiments.