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Two-Grid Finite-Element Method for the Two-Dimensional Time-Dependent Schrödinger Equation

Published online by Cambridge University Press:  03 June 2015

Hongmei Zhang ,
Jicheng Jin  and
Jianyun Wang
Hongmei Zhang*
Affiliation:
School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, Hunan, China School of Science, Hunan University of Technology, Zhuzhou 412007, Hunan, China
Jicheng Jin*
Affiliation:
School of Science, Hunan University of Technology, Zhuzhou 412007, Hunan, China
Jianyun Wang
Affiliation:
School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, Hunan, China
*
Email: zhm10180@yahoo.com.cn
Corresponding author. Email: jcjin2008@sina.com
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Abstract

In this paper, we construct semi-discrete two-grid finite element schemes and full-discrete two-grid finite element schemes for the two-dimensional time-dependent Schrödinger equation. The semi-discrete schemes are proved to be convergent with an optimal convergence order and the full-discrete schemes, verified by a numerical example, work well and are more efficient than the standard finite element method.

Keywords

65N3065N55Schrödinger equationtwo-grid methodfinite element method
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 5 , Issue 2 , April 2013 , pp. 180 - 193
Copyright
Copyright © Global-Science Press 2013

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