Unified Analysis of Leap-Frog Methods for Solving Time-Domain Maxwell’s Equations in Dispersive Media

In this paper, we consider the time dependent Maxwell’s equations resulting from dispersive medium models. First, the stability and Gauss’s law are proved for all three most popular dispersive medium models: the isotropic cold plasma, the one-pole Debye medium and the two-pole Lorentz medium. Then leap-frog mixed finite element methods are developed for these three models. Optimal error estimates are proved for all three models solved by the lowest-order Raviart-Thomas-Nédélec spaces. Extensions to multiple pole dispersive media are presented also. Numerical results confirming the analysis are presented.