New Energy Analysis of Yee Scheme for Metamaterial Maxwell's Equations on Non-Uniform Rectangular Meshes

Abstract

In this paper, several new energy identities of metamaterial Maxwell's equations with the perfectly electric conducting (PEC) boundary condition are proposed and proved. These new energy identities are different from the Poynting theorem. By using these new energy identities, it is proved that the Yee scheme on non-uniform rectangular meshes is stable in the discrete $L^2$ and $H^1$ norms when the Courant-Friedrichs-Lewy (CFL) condition is satisfied. Numerical experiments in two-dimension (2D) and 3D are carried out and confirm our analysis, and the superconvergence in the discrete $H^1$ norm is found.