Time dependent electromagnetic scattering by a penetrable obstacle

We consider time domain electromagnetic scattering from a bounded homogeneous penetrable obstacle. The problem is reduced to a system of time dependent integral equations on the boundary of the scatterer. Using convolution quadrature in time and a Galerkin method on the boundary we derive error estimates for the fully discrete system of boundary integral equations. This is accomplished by proving parameter dependent estimates for the discrete and continuous integral equation system in the Laplace transform domain. In particular a non-standard transmission problem is analyzed. Besides the error estimates, the paper provides a useful extension result and estimates for the spatially semi-discrete problem.