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arXiv · 1703.02281

A Crank-Nicolson Finite Element Method and the Optimal Error Estimates for the modified Time-dependent Maxwell-Schr\"{o}dinger Equations

Chupeng Ma·Liqun Cao
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Abstract

In this paper we consider the initial-boundary value problem for the time-dependent Maxwell-Schr\"{o}dinger 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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Chupeng Ma, Liqun Cao. 2017-03-07. A Crank-Nicolson Finite Element Method and the Optimal Error Estimates for the modified Time-dependent Maxwell-Schr\"{o}dinger Equations. https://arxiv.org/abs/1703.02281

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