Superconvergence of Finite Element Approximations of the Two-Dimensional Cubic Nonlinear Schrodinger Equation

被引：1
|
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：
ADVANCES IN APPLIED MATHEMATICS AND MECHANICS | 2022年 / 14卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Superconvergence; nonlinear Schrodinger equation; finite element method; elliptic projection; DISCONTINUOUS GALERKIN METHODS; DEGREE RECTANGULAR ELEMENTS; MAXWELLS EQUATIONS; ERROR ANALYSIS; DISCRETIZATIONS; SIMULATION; SCHEME; PROOF;
D O I：
10.4208/aamm.OA-2020-0268
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The superconvergence of a two-dimensional time-independent nonlinear Schrodinger equation are analyzed with the rectangular Lagrange type finite element of order k. Firstly, the error estimate and superclose property are given in H-1-norm with order O (h(k+1)) between the finite element solution u(h) and the interpolation function u(I) by use of the elliptic projection operator. Then, the global superconvergence is obtained by the interpolation post-processing technique. In addition, some numerical examples with the order k = 1 and k = 2 are provided to demonstrate the theoretical analysis.
引用
收藏
页码：652 / 665
页数：14
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