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On the reconstruction of discontinuous functions using multiquadric RBF–WENO local interpolation techniques

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  • Aràndiga, Francesc
  • Donat, Rosa
  • Romani, Lucia
  • Rossini, Milvia

Abstract

We discuss several approaches involving the reconstruction of discontinuous one-dimensional functions using parameter-dependent multiquadric radial basis function (MQ-RBF) local interpolants combined with weighted essentially non-oscillatory (WENO) techniques, both in the computation of the locally optimized shape parameter and in the combination of RBF interpolants. We examine the accuracy of the proposed reconstruction techniques in smooth regions and their ability to avoid Gibbs phenomena close to discontinuities. In this paper, we propose a true MQ-RBF–WENO method that does not revert to the classical polynomial WENO approximation near discontinuities, as opposed to what was proposed in Guo and Jung (2017) [12,13]. We present also some numerical examples that confirm the theoretical approximation orders derived in the paper.

Suggested Citation

  • Aràndiga, Francesc & Donat, Rosa & Romani, Lucia & Rossini, Milvia, 2020. "On the reconstruction of discontinuous functions using multiquadric RBF–WENO local interpolation techniques," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 176(C), pages 4-24.
    • Handle: RePEc:eee:matcom:v:176:y:2020:i:c:p:4-24
    DOI: 10.1016/j.matcom.2020.01.018
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    References listed on IDEAS

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    1. Lenarduzzi, Licia & Schaback, Robert, 2017. "Kernel-based adaptive approximation of functions with discontinuities," Applied Mathematics and Computation, Elsevier, vol. 307(C), pages 113-123.
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    Cited by:

    1. Pedro Ortiz & Juan Carlos Trillo, 2021. "A Piecewise Polynomial Harmonic Nonlinear Interpolatory Reconstruction Operator on Non Uniform Grids—Adaptation around Jump Discontinuities and Elimination of Gibbs Phenomenon," Mathematics, MDPI, vol. 9(4), pages 1-19, February.
    2. Aiping Wang & Li Li & Shuli Mei & Kexin Meng, 2020. "Hermite Interpolation Based Interval Shannon-Cosine Wavelet and Its Application in Sparse Representation of Curve," Mathematics, MDPI, vol. 9(1), pages 1-21, December.

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