Error analysis of fully discrete mixed finite element schemes for 3-D Maxwell’s equations in dispersive media

We consider the time dependent Maxwell’s equations in dispersive media in a bounded three-dimensional (3-D) domain. Fully discrete mixed finite element methods are developed for three most popular dispersive media models: i.e., the isotropic cold plasma, the one-pole Debye medium and the two-pole Lorentz medium. Optimal error estimates are proved for those three dispersive media under the assumption that the solutions are smooth enough. Numerical results justifying our analysis are provided. We believe that this is the first error analysis carried out for fully discrete mixed finite element methods for solving 3-D Maxwell’s equations in dispersive media.