Energy-Stability of Time-Domain Finite Element Solutions to Maxwell's Equations with Cubic Polarization

Some theoretical and computational results for energy-stable conformal finite element time-domain discretizations of Maxwell's system of differential equations with a cubic polarization term are presented. The focus is on energy estimates in the full range from the continuous to the semidiscrete to the fully discrete problem. In addition, an optimal estimate of the fully discrete error for the numerical approximation that is free from step size restrictions is given. Finally, some results of computer experiments are demonstrated.