Interior penalty discontinuous Galerkin method for Maxwell's equations:: optimal L2-norm error estimates

We consider the symmetric, interior penalty discontinuous Galerkin ( DG) method for the time-dependent Maxwell's equations in second-order form. In Grote et al. ( 2007, J. Comput. Appl. Math., 204, 375 386), optimal a priori estimates in the DG energy norm were derived, either for smooth solutions on arbitrary meshes or for low-regularity ( singular) solutions on conforming, affine meshes. Here, we show that the DG methods are also optimally convergent in the L-2-norm, on tetrahedral meshes and for smooth material coefficients. The theoretical convergence rates are validated by a series of numerical experiments in two-space dimensions, which also illustrate the usefulness of the interior penalty DG method for time-dependent computational electromagnetics.