Space-time discontinuous Galerkin method for Maxwell's equations

Abstract

A fully discrete discontinuous Galerkin method is introduced for solving time-dependent Maxwell's equations. Distinguished from the Runge-Kutta discontinuous Galerkin method (RKDG) and the finite element time domain method (FETD), in our scheme, discontinuous Galerkinmethods are used to discretize not only the spatial domain but also the temporal domain. The proposed numerical scheme is proved to be unconditionally stable, and a convergent rate script O sign((Δt)r+1 + hk+1/2) is established under the L2-normwhen polynomials of degree atmost r and k are used for temporal and spatial approximation, respectively. Numerical results in both 2-D and 3-D are provided to validate the theoretical prediction. An ultra-convergence of order (Δt)2r+1 in time step is observed numerically for the numerical fluxes w.r.t. temporal variable at the grid points. © 2013 Global-Science Press.