On the stability of the moving least squares approximation and the element-free Galerkin method

被引：109

作者：

Li, Xiaolin ^{[1
]}

Li, Shuling ^{[1
]}

机构：

[1] Chongqing Normal Univ, Coll Math Sci, Chongqing 400047, Peoples R China

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2016年 / 72卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Meshless; Stability; Moving least squares approximation; Element-free Galerkin method; Error estimate; Condition number; BOUNDARY NODE METHOD; PARTICLE METHODS; ERROR ANALYSIS;

D O I：

10.1016/j.camwa.2016.06.047

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the stability of the moving least squares (MLS) approximation and a stabilized MLS approximation is analyzed theoretically and verified numerically. It is shown that the stability of the MLS approximation deteriorates severely as the nodal spacing decreases, while the stability of the stabilized MLS approximation is not affected by the nodal spacing. The stabilized MLS approximation is introduced into the element-free Galerkin (EFG) method to produce a stabilized EFG method. Theoretical error analysis of the stabilized EFG method is provided for boundary value problems with mixed boundary conditions of Dirichlet and Robin type. Numerical examples confirm the theoretical results, and show that the stabilized EFG method has higher computational precision and better stability than the original EFG method. (C) 2016 Elsevier Ltd. All rights reserved.

引用

页码：1515 / 1531

页数：17

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