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Quasi-Interpolation in a Space of C 2 Sextic Splines over Powell–Sabin Triangulations

Author

Listed:
  • Salah Eddargani

    (Department of Applied Mathematics, University of Granada, 18071 Granada, Spain
    MISI Laboratory, Faculty of Sciences and Techniques, Hassan First University of Settat, Settat 26000, Morocco)

  • María José Ibáñez

    (Department of Applied Mathematics, University of Granada, 18071 Granada, Spain)

  • Abdellah Lamnii

    (MISI Laboratory, Faculty of Sciences and Techniques, Hassan First University of Settat, Settat 26000, Morocco)

  • Mohamed Lamnii

    (LANO Laboratory, Faculty of Sciences Oujda, Mohammed First University of Oujda, Oujda 60000, Morocco)

  • Domingo Barrera

    (Department of Applied Mathematics, University of Granada, 18071 Granada, Spain)

Abstract

In this work, we study quasi-interpolation in a space of sextic splines defined over Powell–Sabin triangulations. These spline functions are of class C 2 on the whole domain but fourth-order regularity is required at vertices and C 3 regularity is imposed across the edges of the refined triangulation and also at the interior point chosen to define the refinement. An algorithm is proposed to define the Powell–Sabin triangles with a small area and diameter needed to construct a normalized basis. Quasi-interpolation operators which reproduce sextic polynomials are constructed after deriving Marsden’s identity from a more explicit version of the control polynomials introduced some years ago in the literature. Finally, some tests show the good performance of these operators.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:18:p:2276-:d:636738
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    References listed on IDEAS

    as
    1. 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.
    2. Lamnii, M. & Mraoui, H. & Tijini, A. & Zidna, A., 2014. "A normalized basis for C1 cubic super spline space on Powell–Sabin triangulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 99(C), pages 108-124.
    3. Grošelj, Jan & Krajnc, Marjeta, 2016. "C1 cubic splines on Powell–Sabin triangulations," Applied Mathematics and Computation, Elsevier, vol. 272(P1), pages 114-126.
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