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

页码：652 / 665

页数：14

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