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A meshless superconvergent stabilized collocation method for linear and nonlinear elliptic problems with accuracy analysis

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  • Hou, Huanyang
  • Li, Xiaolin

Abstract

The stabilized collocation method (SCM) is a promising meshless collocation method that can overcome the instability defects in the classical direct collocation method. To improve the performance of the SCM, a superconvergent stabilized collocation method (SSCM) is developed in this paper for linear and nonlinear elliptic problems through the use of the moving least squares (MLS) approximation and its smoothed derivatives. Accuracy of the SSCM and the SCM is analyzed with an emphasis on the influence of boundary conditions, and precise error measures are presented for different types of boundary conditions. Numerical results validate the superconvergence of the SSCM and confirm the theoretical analysis.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:477:y:2024:i:c:s0096300324002625
    DOI: 10.1016/j.amc.2024.128801
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    References listed on IDEAS

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    1. Li, Xiaolin & Dong, Haiyun, 2020. "Error analysis of the meshless finite point method," Applied Mathematics and Computation, Elsevier, vol. 382(C).
    2. Oruç, Ömer, 2021. "A radial basis function finite difference (RBF-FD) method for numerical simulation of interaction of high and low frequency waves: Zakharov–Rubenchik equations," Applied Mathematics and Computation, Elsevier, vol. 394(C).
    3. Sun, Linlin & Fu, Zhuojia & Chen, Zhikang, 2023. "A localized collocation solver based on fundamental solutions for 3D time harmonic elastic wave propagation analysis," Applied Mathematics and Computation, Elsevier, vol. 439(C).
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