An Efficient Discontinuous Galerkin Finite Element Method for Highly Accurate Solution of Maxwell Equations

A discontinuous Galerkin finite element method (DG-FEM) with a highly accurate time integration scheme for solving Maxwell equations is presented. The new time integration scheme is in the form of traditional predictor-corrector algorithms, PE(CE)^m, but it uses coefficients that are obtained using a numerical scheme with fully controllable accuracy. Numerical results demonstrate that the proposed DG-FEM uses larger time steps than DG-FEM with classical PE(CE)^m schemes when high accuracy, which could be obtained using high-order spatial discretization, is required.