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Superconvergent local quasi-interpolants based on special multivariate quadratic spline space over a refined quadrangulation

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  • Sbibih, D.
  • Serghini, A.
  • Tijini, A.

Abstract

In this paper, we first recall some results concerning the construction and the properties of quadratic B-splines over a refinement Δ of a quadrangulation ◊ of a planar domain introduced recently by Lamnii et al. Then we introduce the B-spline representation of Hermite interpolant, in the special space S21,0(Δ), of any polynomial or any piecewise polynomial over refined quadrangulation Δ of ◊. After that, we use this B-representation for constructing several superconvergent discrete quasi-interpolants. The new results that we present in this paper are an improvement and a generalization of those developed in the above cited paper.

Suggested Citation

  • Sbibih, D. & Serghini, A. & Tijini, A., 2015. "Superconvergent local quasi-interpolants based on special multivariate quadratic spline space over a refined quadrangulation," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 145-156.
    • Handle: RePEc:eee:apmaco:v:250:y:2015:i:c:p:145-156
    DOI: 10.1016/j.amc.2014.10.090
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    References listed on IDEAS

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    1. Foucher, Françoise & Sablonnière, Paul, 2009. "Quadratic spline quasi-interpolants and collocation methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(12), pages 3455-3465.
    2. Abbadi, A. & Ibáñez, M.J. & Sbibih, D., 2011. "Computing quasi-interpolants from the B-form of B-splines," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(10), pages 1936-1948.
    3. Fortes, M.A. & Ibáñez, M.J. & Rodríguez, M.L., 2009. "On Chebyshev-type integral quasi-interpolation operators," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(12), pages 3478-3491.
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    Cited by:

    1. Serghini, A., 2021. "A construction of a bivariate C2 spline approximant with minimal degree on arbitrary triangulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 358-371.
    2. Salah Eddargani & María José Ibáñez & Abdellah Lamnii & Mohamed Lamnii & Domingo Barrera, 2021. "Quasi-Interpolation in a Space of C 2 Sextic Splines over Powell–Sabin Triangulations," Mathematics, MDPI, vol. 9(18), pages 1-22, September.
    3. Andrea Raffo & Silvia Biasotti, 2021. "Weighted Quasi-Interpolant Spline Approximations of Planar Curvilinear Profiles in Digital Images," Mathematics, MDPI, vol. 9(23), pages 1-16, November.

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