Sharper electric-field error estimates

Derive sharper electric-field error estimates for the hybridizable discontinuous Galerkin approximations of the four time-modulated Drude–Lorentz Maxwell models, including the effects of temporal switching and the model-2 constitutive field jump.

Background

The principal spatial convergence theorem establishes common-state estimates, while the electric field is reconstructed algebraically from the displacement and material variables. In the polarization-density model, temporal changes in the coupling coefficient can produce an electric-field jump even when the continuous state remains continuous, and displaced switching times can prevent uniform-in-time field convergence. The paper therefore identifies sharper, model-aware electric-field estimates as unresolved beyond the existing state estimates.