Abstract 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.

中文翻译：

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无网格有限点法的误差分析

摘要 有限点法（FPM）是一种基于移动最小二乘法（MLS）近似和点配置技术的真正意义上的无网格方法。本文对FPM的误差进行了理论上的分析。理论结果表明，当前的误差界限与 MLS 近似中使用的节点间距和基函数的阶数直接相关。当前的误差估计与系数矩阵的条件数无关，并改进了先前报告的估计。给出了超过 160000 个节点的数值例子来证实理论结果。