Mathematical and numerical study of wave propagation in negative-index materials

In this paper, we develop a Crank–Nicolson mixed finite element method for modeling wave propagation in negative-index materials (NIMs). The NIMs model is formed as a time-dependent system involving four dependent vector variables: the electric and magnetic fields, and the induced electric and magnetic currents. Optimal error estimates for all four variables are proved for Nédélec edge elements. Numerical examples are presented to show the exotic properties for wave propagation in NIMs.