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Error analysis of the meshless finite point method

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  • Li, Xiaolin
  • Dong, Haiyun

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.

Suggested Citation

  • Li, Xiaolin & Dong, Haiyun, 2020. "Error analysis of the meshless finite point method," Applied Mathematics and Computation, Elsevier, vol. 382(C).
    • Handle: RePEc:eee:apmaco:v:382:y:2020:i:c:s0096300320302927
    DOI: 10.1016/j.amc.2020.125326
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    References listed on IDEAS

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    1. Li, Xiaolin & Dong, Haiyun, 2019. "Analysis of the element-free Galerkin method for Signorini problems," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 41-56.
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    Cited by:

    1. Hou, Huanyang & Li, Xiaolin, 2024. "A meshless superconvergent stabilized collocation method for linear and nonlinear elliptic problems with accuracy analysis," Applied Mathematics and Computation, Elsevier, vol. 477(C).
    2. Liu, Zheng & Wei, Gaofeng & Qin, Shaopeng & Wang, Zhiming, 2022. "The elastoplastic analysis of functionally graded materials using a meshfree RRKPM," Applied Mathematics and Computation, Elsevier, vol. 413(C).

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