A new highly accurate time integration scheme for DG-FEM

A two-dimensional (2-D) discontinuous Galerkin finite element method (DG-FEM), which uses a new highly-accurate predictor-corrector scheme for time integration, is presented. Numerical results show that the new integration scheme uses larger time steps than the fourth-order Runge-Kutta method for simulations with high accuracy. This, when combined with the fact that it requires only two right-hand side evaluations per time step, renders the proposed method quite efficient.