Unified Analysis of Time Domain Mixed Finite Element Methods for Maxwell's Equations in Dispersive Media (Journal of Computational Mathematics, 2019)
In this paper, we consider the time dependent Maxwell's equations when dispersive media are involved. The Crank-Nicolson mixed finite element methods are developed for three most popular dispersive medium models: the isotropic cold plasma, the one-pole Debye medium and the two-pole Lorentz medium. Optimal error estimates are proved for all three models solved by the Raviart-Thomas-Nédélec spaces. Extensions to multiple pole dispersive media are presented also.
Keywords: Maxwell's equations; Dispersive media; Mixed finite element method.