Two-grid algorithm for two-dimensional linear Schrödinger equation by the mixed finite element method

被引：0
|
作者：
Wang, Jianyun [1 ]
Tian, Zhikun [2 ]
机构：
[1] Hunan Univ Technol, Sch Sci, Zhuzhou 412007, Hunan, Peoples R China
[2] Hunan Inst Engn, Sch Computat Sci & Elect, Xiangtan 411104, Hunan, Peoples R China
来源：
RESULTS IN APPLIED MATHEMATICS | 2023年 / 20卷
关键词：
Schrodinger equation; -grid algorithm; Mixed finite element method; Backward Euler scheme; NONLINEAR SCHRODINGER-EQUATION; DISCONTINUOUS GALERKIN METHODS; SUPERCONVERGENCE ANALYSIS; DISCRETIZATION; SCHEME;
D O I：
10.1016/j.rinam.2023.100404
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we propose a new two-grid algorithm for solving two-dimensional Schrodinger equation in semi-discrete and fully discrete mixed finite element scheme, respectively. With this algorithm, the solution of the Schrodinger equation on a fine grid can be reduced to the original problem on a much coarser grid together with two Poisson equations on the fine grid. In addition, we obtain error results of the two-grid solution. At last, a numerical experiment is provided to demonstrate the efficiency of the two-grid algorithm.
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页数：9
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