A Crank-Nicolson Finite Element Method and the Optimal Error Estimates for the modified Time-dependent Maxwell-Schrödinger Equations

2017/03/07 by Ma, Chupeng, Cao, Liqun
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1703.02281

Abstract

In this paper we consider the initial-boundary value problem for the time-dependent Maxwell-Schrödinger equations, which arises in the interaction between the matter and the electromagnetic field for the semiconductor quantum devices. A Crank-Nicolson finite element method for solving the problem is presented. The optimal energy-norm error estimates for the numerical algorithm without any time-step restrictions are derived. Numerical tests are then carried out to confirm the theoretical results.

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