Two-grid method for the two-dimensional time-dependent Schrodinger equation by the finite element method

被引：20
作者：
Tian, Zhikun [1 ,3 ]
Chen, Yanping [2 ]
Huang, Yunqing [1 ]
Wang, Jianyun [4 ]
机构：
[1] Xiangtan Univ, Sch Math & Computat Sci, Hunan Key Lab Computat & Simulat Sci & Engn, Xiangtan 411105, Hunan, Peoples R China
[2] South China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R China
[3] Hunan Inst Engn, Coll Sci, Xiangtan 411104, Hunan, Peoples R China
[4] Hunan Univ Technol, Sch Sci, Zhuzhou 412007, Hunan, Peoples R China
来源：
COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2019年 / 77卷 / 12期
基金：
美国国家科学基金会;
关键词：
Schrodinger equation; Finite element method; Two-grid method; Elliptic projection; NONLINEAR PARABOLIC EQUATIONS; SUPERCONVERGENCE ANALYSIS; DISCRETIZATIONS;
D O I：
10.1016/j.camwa.2019.01.030
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we construct a backward Euler full-discrete two-grid finite element scheme for the two-dimensional time-dependent Schrodinger equation. With this method, the solution of the original problem on the fine grid is reduced to the solution of same problem on a much coarser grid together with the solution of two Poisson equations on the same fine grid. We analyze the error estimate of the standard finite element solution and the two-grid solution in the H-1 norm. It is shown that the two-grid algorithm can achieve asymptotically optimal approximation as long as the mesh sizes satisfy H = O(h k/k+1). Finally, a numerical experiment indicates that our two-grid algorithm is more efficient than the standard finite element method. (C) 2019 Elsevier Ltd. All rights reserved.
引用
收藏
页码：3043 / 3053
页数：11
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