Two-grid mixed finite element method for two-dimensional time-dependent Schrodinger equation

被引：2
|
作者：
Tian, Zhikun [1 ]
Chen, Yanping [2 ]
Huang, Yunqing [3 ]
Wang, Jianyun [4 ]
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] Xiangtan Univ, Sch Math & Coputat Sci, Hunan Key Lab Computat & Simulat Sci & Engn, Xiangtan 411105, Hunan, Peoples R China
[4] Hunan Univ Technol, Sch Sci, Zhuzhou 412007, Hunan, Peoples R China
来源：
MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2023年 / 46卷 / 12期
基金：
中国国家自然科学基金;
关键词：
mixed finite element methods; Schrodinger equation; semidiscrete scheme; two-grid method; GALERKIN METHODS; SUPERCONVERGENCE ANALYSIS; MISCIBLE DISPLACEMENT; SCHEMES;
D O I：
10.1002/mma.9210
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study the semidiscrete mixed finite element scheme and construct a two-grid algorithm for the two-dimensional time-dependent Schrodinger equation. We analyze error results of the mixed finite element solution in L-2-norm by some projection operators. Then, we propose a two-grid method of the semidiscrete mixed finite element. With this method, the solution of the Schrodinger equation on a fine grid is reduced to the solution of original problem on a much coarser grid together with the solution of two elliptic equations on the fine grid. We also obtain the error estimate of two-grid solution with exact solution in L-2-norm. Finally, a numerical experiment indicates that our two-grid algorithm is more efficient than the standard mixed finite element method.
引用
收藏
页码：12759 / 12776
页数：18
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