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Theoretical Analysis of the Reproducing Kernel Gradient Smoothing Integration Technique in Galerkin Meshless Methods

Theoretical Analysis of the Reproducing Kernel Gradient Smoothing Integration Technique in Galerkin Meshless Methods
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Year:    2023

Author:    Xiaolin Li

Journal of Computational Mathematics, Vol. 41 (2023), Iss. 3 : pp. 501–524

Abstract

Numerical integration poses greater challenges in Galerkin meshless methods than finite element methods owing to the non-polynomial feature of meshless shape functions. The reproducing kernel gradient smoothing integration (RKGSI) is one of the optimal numerical integration techniques in Galerkin meshless methods with minimum integration points. In this paper, properties, quadrature rules and the effect of the RKGSI on meshless methods are analyzed. The existence, uniqueness and error estimates of the solution of Galerkin meshless methods under numerical integration with the RKGSI are established. A procedure on how to choose quadrature rules to recover the optimal convergence rate is presented.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.2201-m2021-0361

Journal of Computational Mathematics, Vol. 41 (2023), Iss. 3 : pp. 501–524

Published online:    2023-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    24

Keywords:    Galerkin meshless method Numerical integration Quadrature rule Error estimates Element-free Galerkin method Degree of precision.

Author Details

Xiaolin Li

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