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C 1 -Cubic Quasi-Interpolation Splines over a CT Refinement of a Type-1 Triangulation

Author

Listed:
  • Haithem Benharzallah

    (Department of Mathematics, LTM, University of Batna 2, Mostefa Ben Boulaïd, Fesdis, Batna 05078, Algeria)

  • Abdelaziz Mennouni

    (Department of Mathematics, LTM, University of Batna 2, Mostefa Ben Boulaïd, Fesdis, Batna 05078, Algeria)

  • Domingo Barrera

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

Abstract

C 1 continuous quasi-interpolating splines are constructed over Clough–Tocher refinement of a type-1 triangulation. Their Bernstein–Bézier coefficients are directly defined from the known values of the function to be approximated, so that a set of appropriate basis functions is not required. The resulting quasi-interpolation operators reproduce cubic polynomials. Some numerical tests are given in order to show the performance of the approximation scheme.

Suggested Citation

  • Haithem Benharzallah & Abdelaziz Mennouni & Domingo Barrera, 2022. "C 1 -Cubic Quasi-Interpolation Splines over a CT Refinement of a Type-1 Triangulation," Mathematics, MDPI, vol. 11(1), pages 1-19, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2022:i:1:p:59-:d:1013456
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