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.

引用

页码：298 / 310

页数：13

共 50 条

[1] Unconditional superconvergence analysis of conforming finite element for nonlinear parabolic equation
Shi, Dongyang
Wang, Junjun
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2017, 294 : 216 - 226
[2] Superconvergence analysis for nonlinear Schrodinger equation with two-grid finite element method
Wang, Junjun
Li, Meng
Guo, Lijuan
[J]. APPLIED MATHEMATICS LETTERS, 2021, 122
[3] Superconvergence Analysis of Bilinear Finite Element for the Nonlinear Schrodinger Equation on the Rectangular Mesh
Tian, Zhikun
Chen, Yanping
Wang, Jianyun
[J]. ADVANCES IN APPLIED MATHEMATICS AND MECHANICS, 2018, 10 (02) : 468 - 484
[4] Superconvergence analysis of anisotropic linear triangular finite element for nonlinear Schrodinger equation
Shi Dongyang
Wang Pingli
Zhao Yanmin
[J]. APPLIED MATHEMATICS LETTERS, 2014, 38 : 129 - 134
[5] Superconvergence analysis of finite element method for the time-dependent Schrodinger equation
Wang, Jianyun
Huang, Yunqing
Tian, Zhikun
Zhou, Jie
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2016, 71 (10) : 1960 - 1972
[6] GLOBAL SUPERCONVERGENCE ESTIMATES OF FINITE ELEMENT METHOD FOR SCHRODINGER EQUATION
Qin Lin(Institute of Systems Science
[J]. Journal of Computational Mathematics, 1998, (06) : 521 - 526
[7] Global superconvergence estimates of finite element method for Schrodinger equation
Lin, Q
Liu, XQ
[J]. JOURNAL OF COMPUTATIONAL MATHEMATICS, 1998, 16 (06) : 521 - 526
[8] Superconvergence analysis for a nonlinear parabolic equation with a BDF finite element method
Wang, Junjun
Yang, Xiaoxia
[J]. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2020, 97 (12) : 2487 - 2506
[9] Superconvergence Analysis of Anisotropic Finite Element Method for a Kind of Nonlinear Degenerate Wave Equation
Li, Zhiyan
Liu, Linghui
Qu, Jingguo
Cui, Yuhuan
[J]. INFORMATION COMPUTING AND APPLICATIONS, PT 2, 2010, 106 : 341 - +
[10] Unconditional superconvergence analysis of a new mixed finite element method for nonlinear Sobolev equation
Shi Dongyang
Yan Fengna
Wang Junjun
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2016, 274 : 182 - 194

← 1 2 3 4 5 →