Abstract
The numerical approximation of Maxwell’s equations in Cole–Cole dispersive media is studied for two and three-dimensional cases. We construct a combined scheme using the standard continuous Galerkin (CG) finite element method in time and discontinuous Galerkin (DG) method in space to discretize the Cole–Cole dispersive model. The L2-stability and error estimate of the proposed scheme are analyzed. Furthermore, we use sum-of-exponential approximation for the convolution kernel to speed up the evaluation of the Caputo derivative. Numerical examples are provided to demonstrate the performance of the proposed numerical methods.
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