Fully Discrete Galerkin Finite Element Method for the Cubic Nonlinear Schrodinger Equation

被引：11

作者：

Wang, Jianyun ^{[1
]}

Huang, Yunqing ^{[2
]}

机构：

[1] Hunan Univ Technol, Sch Sci, Zhuzhou 412007, Peoples R China

[2] Xiangtan Univ, Sch Math & Computat Sci, Hunan Key Lab Computat & Simulat Sci & Engn, Xiangtan 411105, Peoples R China

来源：

NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS | 2017年 / 10卷 / 03期

基金：

美国国家科学基金会;

关键词：

Finite element method; nonlinear Schrdinger equations; backward Euler scheme; Crank-Nicolson scheme; NUMERICAL-SOLUTION; DIFFERENCE-SCHEMES; DISCRETIZATIONS; APPROXIMATIONS;

D O I：

10.4208/nmtma.2017.y16008

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with numerical method for a two-dimensional timedependent cubic nonlinear Schrodinger equation. The approximations are obtained by the Galerkin finite element method in space in conjunction with the backward Euler method and the Crank-Nicolson method in time, respectively. We prove optimal L-2 error estimates for two fully discrete schemes by using elliptic projection operator. Finally, a numerical example is provided to verify our theoretical results.

引用

页码：671 / 688

页数：18

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