The Super Convergence Analysis Of A Non-local Dispersion Model For Light Interaction With Metallic Nanostructures

In this paper, a non-local dispersion model for light interaction with metallic nanos-tructures is discussed by the superconvergence analysis, which couples the time-domain Maxwell's equations to another two partial differential equations. The stability and the superclose analysis of the backward Euler scheme and Crank-Nicolson scheme are estab-lished by using arbitrary orders of Raviart-Thomas- Nedelec element, respectively. The superclose analysis of the leap-frog scheme is also provided. Then the global supercon-vergence is demonstrated after presenting the interpolation post-processing operators. At the same time, some asymptotic expansion formulas are derived by Hilbert-Branmble-Xu Lemma, which is an important tool of the superconvergence analysis. For the convenience,the spatial convergence is improved from O(h) to O(h1.5) for the lowest order Raviart-Thomas- Nedelec element. In the end, numerical example of transverse electrical model is presented to verify our theoretical analysis.