Analysis of Stability and Dispersion in a Finite Element Method for Debye and Lorentz Dispersive Media

We study the stability properties of, and the phase error present in, a finite element scheme for Maxwell’s equations coupled with a Debye or Lorentz polarization model. In one dimension we consider a second order formulation for the electric field with an ordinary differential equation for the electric polarization added as an auxiliary constraint. The finite element method uses linear finite elements in space for the electric field as well as the electric polarization, and a theta scheme for the time discretization. Numerical experiments suggest the method is unconditionally stable for both Debye and Lorentz models. We compare the stability and phase error properties of the method presented here with those of finite difference methods that have been analyzed in the literature.We also conduct numerical simulations that verify the stability and dispersion properties of the scheme. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 00: 000–000, 2008