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On the Convexity Preservation of a Quasi C 3 Nonlinear Interpolatory Reconstruction Operator on σ Quasi-Uniform Grids

Author

Listed:
  • Pedro Ortiz

    (Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, 30202 Cartagena, Spain)

  • Juan Carlos Trillo

    (Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, 30202 Cartagena, Spain)

Abstract

This paper is devoted to introducing a nonlinear reconstruction operator, the piecewise polynomial harmonic (PPH), on nonuniform grids. We define this operator and we study its main properties, such as its reproduction of second-degree polynomials, approximation order, and conditions for convexity preservation. In particular, for σ quasi-uniform grids with σ ≤ 4 , we get a quasi C 3 reconstruction that maintains the convexity properties of the initial data. We give some numerical experiments regarding the approximation order and the convexity preservation.

Suggested Citation

  • Pedro Ortiz & Juan Carlos Trillo, 2021. "On the Convexity Preservation of a Quasi C 3 Nonlinear Interpolatory Reconstruction Operator on σ Quasi-Uniform Grids," Mathematics, MDPI, vol. 9(4), pages 1-18, February.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:4:p:310-:d:493223
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    Cited by:

    1. Amat, S. & Ortiz, P. & Ruiz, J. & Trillo, J.C. & Yáñez, D.F., 2023. "The translation operator. Applications to nonlinear reconstruction operators on nonuniform grids," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 408-424.

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