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

摘要

We study the stability properties of, and the phase error present in, a nite element scheme for Maxwell's equations coupled with Debye or Lorentz polarization. In one dimension we consider a second order formulation for the electric eld with an ordinary di erential equation for the polarization added as an auxiliary constraint. The nite element method uses linear nite elements in space for the electric eld as well as the 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 nite di erence methods that have been analyzed in the literature. We also conduct numerical simulations that verify the stability and dispersion properties of the scheme.