Analysis and application of the nodal discontinuous Galerkin method for wave propagation in metamaterials

In this paper, we develop a nodal discontinuous Galerkin method for solving the time-dependent Maxwellʼs equations when metamaterials are involved. Both semi- and fully-discrete schemes are constructed. Numerical stability and error estimate are proved for both schemes. Numerical results are presented to demonstrate that the method is not only efficient but also very effective in solving metamaterial Maxwellʼs equations.