High-order time integration Leap-Frog schemes combined with a discontinuous Galerkin method for the solution of the Maxwell equations

Abstract : In this report, after pedagogical mathematical insight into basic notions of numerical analysis for differential equations, more specific Discontinuous Galerkin (DG) method is introduced. Afterwards, the DG method is combined with a fourth-order staggered Leap-Frog (LF4) scheme to be applied to the solution of the Maxwell equations wave-propagation problem. Stability analysis of the resulting scheme is performed and some peculiarities related with the choice of basis functions in the DG method are stressed.