IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v203y2023icp408-424.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475422002439
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2022.05.031?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.

      Corrections

      All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matcom:v:203:y:2023:i:c:p:408-424. See general information about how to correct material in RePEc.

      If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

      If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

      If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

      For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

      Please note that corrections may take a couple of weeks to filter through the various RePEc services.

      IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.