Error analysis of the meshless finite point method

• Published in: Applied mathematics and computation Vol. 382; p. 125326
• Main Authors: Li, Xiaolin, Dong, Haiyun
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.10.2020
• Subjects: Condition number; Error estimates; Finite point method; Meshless methods; Moving least squares approximation; Condition number; Moving least squares approximation; Error estimates; Finite point method; Meshless methods
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2020.125326

•A new error estimation is established theoretically for the meshlessnite point method.•The error bound is directly related to the nodal spacing and the order of basis functions.•Theoretical and numerical results show that the present estimation improves the previously reported estimations. 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.