In this paper, we consider the time dependent Maxwell’s equations
in dispersive media on a bounded three-dimensional domain. Global superconvergence
is obtained for semi-discrete mixed finite element methods for three
most popular dispersive media models: the isotropic cold plasma, the one-pole
Debye medium, and the two-pole Lorentz medium. Global superconvergence
for a standard finite element method is also presented. To our best knowledge,
this is the first superconvergence analysis obtained for Maxwell’s equations
when dispersive media are involved.