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Chin. Phys. B, 2017, Vol. 26(3): 030203    DOI: 10.1088/1674-1056/26/3/030203
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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
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.
Keywords:  meshless method      moving least squares approximation      element-free Galerkin method      error estimate  
Received:  25 October 2016      Revised:  30 November 2016      Published:  05 March 2017
PACS:  02.60.Cb (Numerical simulation; solution of equations)  
  02.60.Lj (Ordinary and partial differential equations; boundary value problems)  
  02.30.Em (Potential theory)  
Fund: 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).
Corresponding Authors:  Xiao-Lin Li     E-mail:  lxlmath@163.com

Cite this article: 

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 2017 Chin. Phys. B 26 030203

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