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.

引用

页数：9

共 38 条

[1] ON FULLY DISCRETE GALERKIN METHODS OF 2ND-ORDER TEMPORAL ACCURACY FOR THE NONLINEAR SCHRODINGER-EQUATION [J].