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Superconvergence analysis of conforming finite element method for nonlinear Schrodinger equation

被引：23
|
作者：
Shi, Dongyang [1 ]
Liao, Xin [1 ]
Wang, Lele [1 ]
机构：
[1] Zhengzhou Univ, Sch Math & Stat, Zhengzhou 450001, Peoples R China
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2016年 / 289卷
基金：
中国国家自然科学基金;
关键词：
Nonlinear Schrodinger equation; Bilinear element; Fully-discrete scheme; Supercloseness and superconvergence; NUMERICAL-SOLUTION; GALERKIN METHOD;
D O I：
10.1016/j.amc.2016.05.020
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The main aim of this paper is to apply the conforming bilinear finite element to solve the nonlinear Schrodinger equation (NLSE). Firstly, the stability and convergence for time discrete scheme are proved. Secondly, through a new estimate approach, the optimal order error estimates and superclose properties in H-1-norm are obtained with Backward Euler (B-E) and Crank-Nicolson (C-N) fully-discrete schemes, the global superconvergence results are deduced with the help of interpolation postprocessing technique. Finally, some numerical examples are provided to verify the theoretical analysis. (C) 2016 Elsevier Inc. All rights reserved.
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页码：298 / 310
页数：13
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