  In this paper we propose and analyze finite element discontinuous Galerkin
methods for the one- and two-dimensional stochastic Maxwell equations with
multiplicative noise. The discrete energy law of the semi-discrete DG methods
were studied. Optimal error estimate of the semi-discrete method is obtained
for the one-dimensional case, and the two-dimensional case on both rectangular
meshes and triangular meshes under certain mesh assumptions. Strong Taylor 2.0
scheme is used as the temporal discretization. Both one- and two-dimensional
numerical results are presented to validate the theoretical analysis results.
