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Research on Error Estimations of the Interpolating Boundary Element Free-Method for Two-Dimensional Potential Problems

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  • Jufeng Wang
  • Fengxin Sun
  • Ying Xu

Abstract

The interpolating boundary element-free method (IBEFM) is a direct solution method of the meshless boundary integral equation method, which has high efficiency and accuracy. The IBEFM is developed based on the interpolating moving least-squares (IMLS) method and the boundary integral equation method. Since the shape function of the IMLS method satisfies the interpolation characteristics, the IBEFM can directly and accurately impose the essential boundary conditions, which overcomes the shortcomings of the original boundary element-free method in enforcing the essential boundary approximately. This paper will study the error estimations of the IBEFM for two-dimensional potential problems and the relationship between the errors and the influence radius and the condition number of the coefficient matrix. Two numerical examples are presented to verify the correctness of the theoretical results in this paper.

Suggested Citation

  • Jufeng Wang & Fengxin Sun & Ying Xu, 2020. "Research on Error Estimations of the Interpolating Boundary Element Free-Method for Two-Dimensional Potential Problems," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-10, July.
    • Handle: RePEc:hin:jnlmpe:6378745
    DOI: 10.1155/2020/6378745
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    Cited by:

    1. Jufeng Wang & Fengxin Sun & Rongjun Cheng, 2021. "A Dimension Splitting-Interpolating Moving Least Squares (DS-IMLS) Method with Nonsingular Weight Functions," Mathematics, MDPI, vol. 9(19), pages 1-22, September.
    2. Fengxin Sun & Jufeng Wang & Xiang Kong & Rongjun Cheng, 2021. "A Dimension Splitting Generalized Interpolating Element-Free Galerkin Method for the Singularly Perturbed Steady Convection–Diffusion–Reaction Problems," Mathematics, MDPI, vol. 9(19), pages 1-15, October.

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