An analysis of the Leap-Frog Discontinuous Galerkin method for Maxwell equations

Abstract

In this paper, we explore the accuracy limits of a Finite-Element Time-Domain 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 Time-Domain methods. A comparison with the Finite-Difference Time-Domain method, in terms of computational cost, is also included