Superconvergence analysis of Yee scheme for metamaterial Maxwell's equations on non-uniform rectangular meshes (Q342888)

The paper deals with the convergence analysis of the FDTD (finite difference time-domain) method on staggered non-uniform rectangular grids for solving Maxwell equations for bounded domains with metamaterials. The authors prove stability for both the semi- and fully-discrete schemes and establish superconvergence, i.e., second-oder convergence in space and time. They extend methods and results of \textit{P. Monk} and \textit{E. Süli} [SIAM J. Numer. Anal. 31, No. 2, 393--412 (1994; Zbl 0805.65121)] concerning superconvergence of the semi-discrete scheme for Maxwell equations without metamaterials. Two numerical examples support the theoretical analysis and demonstrate the backward wave propagation in a metamaterial slab.