An Analysis of the Leap-Frog Discontinuous Galerkin Method for Maxwell's Equations

In this paper, we explore the accuracy limits of a finite-element time-domain (TD) method applied to the Maxwell equations, based on a discontinuous Galerkin scheme in space, and a leap-frog temporal integration. The dispersion and dissipation properties of the method are investigated, as well as the anisotropy of the errors. The results of this novel analysis are represented in a practical and comprehensible manner, useful for the application of the method, and for the understanding of the behavior of the errors in discontinuous Gelerkin TD methods. A comparison with the finite-difference TD method, in terms of computational cost, is also included.