Stability of a Leap-Frog Discontinuous Galerkin Method for Time-Domain Maxwell's Equations in Anisotropic Materials (Communications in Computational Physics, 2018)
In this work we discuss the numerical discretization of the time-dependentMaxwell's equations using a fully explicit leap-frog type discontinuous Galerkinmethod. We present a sufficient condition for the stability and error estimates, forcases of typical boundary conditions, either perfect electric, perfect magnetic or firstorder Silver-Müller. The bounds of the stability region point out the influence of notonly the mesh size but also the dependence on the choice of the numerical flux and thedegree of the polynomials used in the construction of the finite element space, makingpossible to balance accuracy and computational efficiency. In the model we considerheterogeneous anisotropic permittivity tensors which arise naturally in many applicationsof interest. Numerical results supporting the analysis are provided.