Banks, H. T.; Bokil, V. A.; Gibson, N. L. Analysis of stability and dispersion in a finite element method for Debye and Lorentz dispersive media. (English) Zbl 1168.78314 Numer. Methods Partial Differ. Equations 25, No. 4, 885-917 (2009). Summary: 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. Cited in 29 Documents MSC: 78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory 78M20 Finite difference methods applied to problems in optics and electromagnetic theory 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 78A40 Waves and radiation in optics and electromagnetic theory Keywords:Maxwell’s equations; Debye; Lorentz; finite elements; FDTD; dissipation; dispersion PDFBibTeX XMLCite \textit{H. T. Banks} et al., Numer. Methods Partial Differ. 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