In this paper, we consider the time-dependent Maxwell's equations when Cole-Cole dispersive medium is involved. The Cole-Cole model contains a fractional time derivative term, which couples with the standard Maxwell's equations in free space and creates some challenges in developing and analyzing time-domain finite element methods for solving this model as mentioned in our earlier work [J. Li, J. Sci. Comput., 47 (2001), pp. 1-26]. By adopting some techniques developed for the fractional

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... on equations [V.we propose two fully discrete mixed finite element schemes for the Cole-Cole model. Numerical stability and optimal error estimates are proved for both schemes. The proposed algorithms are implemented and detailed numerical results are provided to justify our theoretical analysis.