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In this work we discuss the numerical discretization of the time-dependentMaxwell's equations using a fully explicit leap-frog type discontinuousGalerkin method. We present a sufficient condition for the stability, for casesof typical boundary conditions, either perfect electric, perfect magnetic orfirst order Silver-M\"uller. The bounds of the stability region point out theinfluence of not only the mesh size but also the dependence on the choice ofthe numerical flux and the degree of the polynomials used in the constructionof the finite element space, making possible to balance accuracy andcomputational efficiency. In the model we consider heterogeneous anisotropicpermittivity tensors which arise naturally in many applications of interest.Numerical results supporting the analysis are provided.

Stability of a leap-frog discontinuous Galerkin method for time-domain Maxwell's equations in anisotropic materials