Two-grid method for two-dimensional nonlinear Schrodinger equation by mixed finite element method

被引：22
|
作者：
Hu, Hanzhang [1 ]
机构：
[1] Jiaying Univ, Sch Math, Meizhou 514015, Guangdong, Peoples R China
来源：
COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2018年 / 75卷 / 03期
基金：
美国国家科学基金会;
关键词：
Schrodinger equation; Two-grid method; Conservative; Convergence; Mixed finite element method; REACTION-DIFFUSION EQUATIONS; WAVE OPERATOR; DIFFERENCE SCHEME; ELLIPTIC-EQUATIONS; COMPACT;
D O I：
10.1016/j.camwa.2017.10.018
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A conservative two-grid mixed finite element scheme is presented for two-dimensional nonlinear Schrodinger equation. One Newton iteration is applied on the fine grid to linearize the fully discrete problem using the coarse-grid solution as the initial guess. Moreover, error estimates are conducted for the two-grid method. It is shown that the coarse space can be extremely coarse, with no loss in the order of accuracy, and still achieve the asymptotically optimal approximation as long as the mesh sizes satisfy H = O(h(1/2)) in the two-grid method. The numerical results show that this method is very effective. (C) 2017 Elsevier Ltd. All rights reserved.
引用
收藏
页码：900 / 917
页数：18
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