Error analysis of the meshless finite point method

被引：36
作者：
Li, Xiaolin [1 ]
Dong, Haiyun [2 ]
机构：
[1] Chongqing Normal Univ, Sch Math Sci, Chongqing 400047, Peoples R China
[2] Chongqing Univ, Coll Math & Stat, Chongqing 400044, Peoples R China
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2020年 / 382卷
基金：
中国国家自然科学基金;
关键词：
Meshless methods; Finite point method; Moving least squares approximation; Error estimates; Condition number; FREE GALERKIN METHOD; APPROXIMATION;
D O I：
10.1016/j.amc.2020.125326
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The finite point method (FPM) is a notable truly meshless method based on the moving least squares (MLS) approximation and the point collocation technique. In this paper, the error of the FPM is analyzed theoretically. Theoretical results show that the present error bound is directly related to the nodal spacing and the order of basis functions used in the MLS approximation. The present error estimation is independent of the condition number of the coefficient matrix and improves the previously reported estimations. Numerical examples with more than 160000 nodes are given to confirm the theoretical result. (C) 2020 Elsevier Inc. All rights reserved.
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页数：12
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