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