Superconvergence Analysis of Bilinear Finite Element for the Nonlinear Schrodinger Equation on the Rectangular Mesh

被引：14
|
作者：
Tian, Zhikun [1 ,4 ]
Chen, Yanping [2 ]
Wang, Jianyun [3 ]
机构：
[1] Xiangtan Univ, Sch Math & Computat Sci, Xiangtan 411105, Hunan, Peoples R China
[2] South China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R China
[3] Hunan Univ Technol, Sch Sci, Zhuzhou 412007, Hunan, Peoples R China
[4] Hunan Inst Engn, Coll Sci, Xiangtan 411104, Hunan, Peoples R China
来源：
ADVANCES IN APPLIED MATHEMATICS AND MECHANICS | 2018年 / 10卷 / 02期
基金：
美国国家科学基金会;
关键词：
Finite element method; nonlinear Schrodinger equation; superconvergence; interpolation post-processing; GALERKIN METHODS; DIFFERENCE METHOD; WAVE OPERATOR; APPROXIMATION;
D O I：
10.4208/aamm.OA-2017-0156
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we investigate the superconvergence property of a time-dependent nonlinear Schrodinger equation with the bilinear finite element method on the rectangular mesh. We prove the superclose error estimate in H-1-norm with order O(h(2)) between the approximated solution and the elliptic projection of the exact solution. Moreover, we obtain the global superconvergence result in H-1-norm with order O(h(2)) by the interpolation post-processing operator.
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页码：468 / 484
页数：17
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