A Crank-Nicolson Finite Element Method and the Optimal Error Estimates for the modified Time-dependent Maxwell-Schr\"{o}dinger Equations
Numerical Analysis
2017-03-08 v1
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.
Keywords
Cite
@article{arxiv.1703.02281,
title = {A Crank-Nicolson Finite Element Method and the Optimal Error Estimates for the modified Time-dependent Maxwell-Schr\"{o}dinger Equations},
author = {Chupeng Ma and Liqun Cao},
journal= {arXiv preprint arXiv:1703.02281},
year = {2017}
}