Superconvergence analysis for time-domain Maxwell's equations in a Havriliak-Negami dispersive medium

In this paper, we develop a mixed finite element method (MFEM) for solving the time-dependent Maxwell's equations in a Havriliak-Negami (H-N) dispersive medium. Firstly, we show that the fully discrete backward Euler scheme is un-conditionally stable. Furthermore, the global superconvergence results are derived with the aid of interpolation postprocessing techniques. To our best knowledge, there is no work in any other publications that discusses the superconvergence error analysis of MFEM for the H-N model. Finally, numerical experiments in two dimensions are provided to verify that the theoretical analysis is well documented. & COPY; 2023 Elsevier Ltd. All rights reserved.

Automated summary

In this paper, a mixed finite element method (MFEM) is developed for solving the time-dependent Maxwell's equations in a Havriliak-Negami (H-N) dispersive medium. The unconditional stability of the fully discrete backward Euler scheme is proven, and global superconvergence results are obtained using interpolation postprocessing techniques. Numerical experiments in two dimensions are provided to demonstrate the validity of the theoretical analysis, which has not been discussed in any other publications.