Finite element study of time‐dependent Maxwell's equations in dispersive media

In this article, we consider the time‐dependent Maxwell's equations in a bounded domain when dispersive media are involved. The Crank‐Nicolson scheme is developed to approximate the electric field equation by Nedelec edge elements and is proved to be optimal convergent in energy norm. The analysis is carried out for Debye medium, but the same results hold true for other dispersive media such as plasma and Lorentz medium. Furthermore, our analysis extends straightforward to cases when a dispersive medium and a simple medium (such as air) are coupled. Mathematics Subject Classification (2000): 65N30, 35L15, 78‐08. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008