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Adaptive RBF-FD method for elliptic problems with point singularities in 2D

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  • Oanh, Dang Thi
  • Davydov, Oleg
  • Phu, Hoang Xuan

Abstract

We describe and test numerically an adaptive meshless generalized finite difference method based on radial basis functions that competes well with the finite element method on standard benchmark problems with reentrant corners of the boundary, sharp peaks and rapid oscillations in the neighborhood of an isolated point. This is achieved thanks to significant improvements introduced into the earlier algorithms of Davydov and Oanh (2011), including a new error indicator of Zienkiewicz–Zhu type.

Suggested Citation

  • Oanh, Dang Thi & Davydov, Oleg & Phu, Hoang Xuan, 2017. "Adaptive RBF-FD method for elliptic problems with point singularities in 2D," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 474-497.
    • Handle: RePEc:eee:apmaco:v:313:y:2017:i:c:p:474-497
    DOI: 10.1016/j.amc.2017.06.006
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    1. Nguyen, Vinh Phu & Rabczuk, Timon & Bordas, Stéphane & Duflot, Marc, 2008. "Meshless methods: A review and computer implementation aspects," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 763-813.
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    Cited by:

    1. Cavoretto, Roberto & De Rossi, Alessandra, 2020. "Error indicators and refinement strategies for solving Poisson problems through a RBF partition of unity collocation scheme," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    2. Cavoretto, Roberto & De Rossi, Alessandra, 2020. "Adaptive procedures for meshfree RBF unsymmetric and symmetric collocation methods," Applied Mathematics and Computation, Elsevier, vol. 382(C).

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