Abstract
In this paper, a novel system of Maxwell–Schrödinger equations with nonlocal effect in metamaterials is derived from the Drude model, hydrodynamical model and Schrödinger equation. A leap-frog finite element scheme, which can be solved one by one efficiently, is constructed by presenting a group of initial values. This scheme is proved to be stable conditionally in energy norm. It is confirmed that the error convergent rate is O(τ2+hr) by splitting the proof into three parts, where τ is the time step, h is the mesh size and r is the maximum total degree of polynomials in finite element spaces. Finally, some numerical results are given to verify the theories.
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