A leap-frog finite element method for wave propagation of Maxwell–Schrödinger equations with nonlocal effect in metamaterials. (15th May 2021)

• Record Type: Journal Article
• Authors: Yao, C.H.; Wang, Z.Y.; Zhao, Y.M.
• Is Part Of: Computers & mathematics with applications. Volume 90(2021)
• Page Start: 25
• Page End: 37
• Publication Date: 2021-05-15
• Subjects: Nonlocal effect -- Maxwell–Schrödinger equations -- Metamaterials -- Stability -- Error estimates; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2021.02.019
• Languages: English
• ISSNs: 0898-1221

Abstract

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 ( τ 2 + h r ) 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.