Two-Grid Method for a Fully Discrete Mixed Finite Element Solution of the Time-Dependent Schrodinger Equation

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, Peoples R China
[2] South China Normal Univ, Sch Math Sci, Guangzhou 510631, Peoples R China
[3] Hunan Univ Technol, Sch Sci, Zhuzhou 412007, Peoples R China
来源：
MATHEMATICS | 2023年 / 11卷 / 14期
基金：
中国国家自然科学基金;
关键词：
two-grid method; Schrodinger equation; mixed finite element method; backward Euler scheme; 4TH-ORDER COMPACT; GALERKIN METHODS; APPROXIMATIONS; SCHEMES;
D O I：
10.3390/math11143127
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study the backward Euler fully discrete mixed finite element method for the time-dependent Schrodinger equation; the error result of the mixed finite element solution is obtained in the L-2-norm with order O(t+h(k+1)). Then, a two-grid method is presented with a backward Euler fully discrete scheme. Using this method, we solve the original problem on a much coarser grid and solve elliptic equations on a fine grid. In addition, the error of the two-grid solution is also obtained in the L-2-norm with order O(t+h(k+1)+Hk+2). The numerical experiment is provided to demonstrate the efficiency of the algorithm.
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页数：14
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