A Novel Space-time Discontinuous Galerkin Method for Solving of One-dimensional Electromagnetic Wave Propagations

In this paper we propose a high-order space-time discontinuous Galerkin (STDG) method for solving of one-dimensional electromagnetic wave propagations in homogeneous medium. The STDG method uses finite element Discontinuous Galerkin discretizations in spatial and temporal domain simultaneously with high order piecewise Jacobi polynomial as the basis functions. The algebraic equations are solved using Block Gauss-Seidel iteratively in each time step. The STDG method is unconditionally stable, so the CFL number can be chosen arbitrarily. Numerical examples show that the proposed STDG method is of exponentially accuracy in time