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Journal of Computational Mathematics ›› 2023, Vol. 41 ›› Issue (3): 502-525.DOI: 10.4208/jcm.2201-m2021-0361

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THEORETICAL ANALYSIS OF THE REPRODUCING KERNEL GRADIENT SMOOTHING INTEGRATION TECHNIQUE IN GALERKIN MESHLESS METHODS

Xiaolin Li   

  1. School of Mathematical Sciences, Chongqing Normal University, Chongqing 400047, China
  • Received:2021-12-20 Revised:2022-01-12 Published:2023-03-14
  • Supported by:
    This work was supported by the National Natural Science Foundation of China (Grant No. 11971085) and the Natural Science Foundation of Chongqing (Grant No. cstc2021jcyj-jqX0011).
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Xiaolin Li. THEORETICAL ANALYSIS OF THE REPRODUCING KERNEL GRADIENT SMOOTHING INTEGRATION TECHNIQUE IN GALERKIN MESHLESS METHODS[J]. Journal of Computational Mathematics, 2023, 41(3): 502-525.

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

CLC Number: 

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