A two-grid discretization method for nonlinear Schrodinger equation by mixed finite element methods

被引：1

作者：

Tian, Zhikun ^{[1
]}

Chen, Yanping ^{[2
]}

Wang, Jianyun ^{[3
]}

机构：

[1] Hunan Inst Engn, Sch Computat Sci & Elect, Xiangtan 411104, 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

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2023年 / 130卷

关键词：

Nonlinear Schrodinger equation; Two-grid; Mixed finite element methods; Semi-discrete scheme; DISCONTINUOUS GALERKIN METHODS; SUPERCONVERGENCE ANALYSIS; MISCIBLE DISPLACEMENT; APPROXIMATIONS; SCHEMES;

D O I：

10.1016/j.camwa.2022.11.015

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we investigate a two-grid discretization method for the two-dimensional time-dependent nonlinear Schrodinger equation by mixed finite element methods. Firstly, we solve original nonlinear Schrodinger equation on a much coarser grid. Then, we solve linear Schrodinger equation on the fine grid. We also propose the error estimate of the two-grid solution with the exact solution in L-2-norm with order O(h(k+1) + H2k+2). It is shown that our two-grid algorithm can achieve asymptotically optimal approximations as long as the mesh sizes satisfy h = O(H-2). Finally, two numerical experiments in the RT0 space are provided to partly verify the accuracy and efficiency of the two-grid algorithm.

引用

页码：10 / 20

页数：11

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