Convergence of a finite element scheme for the two-dimensional time-dependent Schrodinger equation in a long strip

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:234

Article

Jin, Jicheng¹  Wu, Xiaonan² 

[1] Hunan Univ Technol, Sch Sci, Zhuzhou City, Hunan, Peoples R China

[2] Hong Kong Baptist Univ, Dept Math, Kowloon Tong, Hong Kong, Peoples R China

关键词: Schrodinger equation;    Finite element method;    Artificial boundary condition;   

DOI  :  10.1016/j.cam.2010.01.042

来源: Elsevier

【 摘 要 】

This paper addresses the finite element method for the two-dimensional time-dependent Schrodinger equation on an infinite strip by using artificial boundary conditions. We first reduce the original problem into an initial-boundary value problem in a bounded domain by introducing a transparent boundary condition, then fully discretize this reduced problem by applying the Crank-Nicolson scheme in time and a bilinear or quadratic finite element approximation in space. This scheme, by a rigorous analysis, has been proved to be unconditionally stable and convergent, and its convergence order has also been obtained. Finally, two numerical examples are given to verify the accuracy of the scheme. (C) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

Free