Meshless analysis of an improved element-free Galerkin method for linear and nonlinear elliptic problems

doi:10.1088/1674-1056/26/3/030203

中国物理B ›› 2017, Vol. 26 ›› Issue (3): 30203-030203.doi: 10.1088/1674-1056/26/3/030203

Meshless analysis of an improved element-free Galerkin method for linear and nonlinear elliptic problems

Yao-Zong Tang(唐耀宗), Xiao-Lin Li(李小林)

1 College of Mathematics and Statistics, Kashgar University, Kashgar 844000, China;
2 College of Mathematics Science, Chongqing Normal University, Chongqing 400047, China

收稿日期:2016-10-25 修回日期:2016-11-30 出版日期:2017-03-05 发布日期:2017-03-05
通讯作者: Xiao-Lin Li E-mail:lxlmath@163.com
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11471063), the Chongqing Research Program of Basic Research and Frontier Technology, China (Grant No. cstc2015jcyjBX0083), and the Educational Commission Foundation of Chongqing City, China (Grant No. KJ1600330).

Meshless analysis of an improved element-free Galerkin method for linear and nonlinear elliptic problems

Yao-Zong Tang(唐耀宗)¹, Xiao-Lin Li(李小林)²

1 College of Mathematics and Statistics, Kashgar University, Kashgar 844000, China;
2 College of Mathematics Science, Chongqing Normal University, Chongqing 400047, China

Received:2016-10-25 Revised:2016-11-30 Online:2017-03-05 Published:2017-03-05
Contact: Xiao-Lin Li E-mail:lxlmath@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11471063), the Chongqing Research Program of Basic Research and Frontier Technology, China (Grant No. cstc2015jcyjBX0083), and the Educational Commission Foundation of Chongqing City, China (Grant No. KJ1600330).

摘要/Abstract

摘要： We first give a stabilized improved moving least squares (IMLS) approximation, which has better computational stability and precision than the IMLS approximation. Then, analysis of the improved element-free Galerkin method is provided theoretically for both linear and nonlinear elliptic boundary value problems. Finally, numerical examples are given to verify the theoretical analysis.

关键词: meshless method, moving least squares approximation, element-free Galerkin method, error estimate

Abstract: We first give a stabilized improved moving least squares (IMLS) approximation, which has better computational stability and precision than the IMLS approximation. Then, analysis of the improved element-free Galerkin method is provided theoretically for both linear and nonlinear elliptic boundary value problems. Finally, numerical examples are given to verify the theoretical analysis.

Key words: meshless method, moving least squares approximation, element-free Galerkin method, error estimate

中图分类号: (Numerical simulation; solution of equations)

02.60.Cb

02.60.Lj (Ordinary and partial differential equations; boundary value problems) 02.30.Em (Potential theory)

唐耀宗, 李小林. Meshless analysis of an improved element-free Galerkin method for linear and nonlinear elliptic problems[J]. 中国物理B, 2017, 26(3): 30203-030203.

Yao-Zong Tang(唐耀宗), Xiao-Lin Li(李小林). Meshless analysis of an improved element-free Galerkin method for linear and nonlinear elliptic problems[J]. Chin. Phys. B, 2017, 26(3): 30203-030203.

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Meshless analysis of an improved element-free Galerkin method for linear and nonlinear elliptic problems

Meshless analysis of an improved element-free Galerkin method for linear and nonlinear elliptic problems

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