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The translation operator. Applications to nonlinear reconstruction operators on nonuniform grids

Author

Listed:
  • Amat, S.
  • Ortiz, P.
  • Ruiz, J.
  • Trillo, J.C.
  • Yáñez, D.F.

Abstract

In this paper, we define a translation operator in a general form to allow for the application of the weighted harmonic mean in different applications. We outline the main steps to follow to define adapted methods using this tool. We give a practical example by improving the behavior of a nonlinear reconstruction operator defined in nonuniform grids, which was initially meant to work well with strictly convex data. With this improvement, the reconstruction can be now applied to data coming from smooth functions, retaining the expected maximum approximation order even around the inflection point areas, and maintaining convexity properties of the initial data. This adaptation can be carried out for general nonuniform grids, although to get the theoretical results about the approximation order, we require to work with quasi-uniform grids. We check the theoretical results through some numerical experiments.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:203:y:2023:i:c:p:408-424
    DOI: 10.1016/j.matcom.2022.05.031
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    References listed on IDEAS

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    1. 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.
    2. 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.
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