IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-642-33134-3_45.html
   My bibliography  Save this book chapter

Nodal Interpolation Between First-Order Finite Element Spaces in 1D is Uniformly H 1-Stable

In: Numerical Mathematics and Advanced Applications 2011

Author

Listed:
  • T. Dickopf

    (University of Lugano, Institute of Computational Science)

Abstract

This paper is about the stability w.r.t. the H 1-semi-norm of the nodal interpolation operator acting between non-nested finite element spaces. (An earlier, slightly less general version of the main result has been proved in the author’s thesis (Dickopf, Multilevel methods based on non-nested meshes. Ph.D. thesis, University of Bonn, 2010. http://hss.ulb.uni-bonn.de/2010/2365 , Chap. 5.1). Lively and fruitful discussions first during the ENUMATH conference in September and then during the Söllerhaus Workshop on Domain Decomposition Methods in October 2011 have encouraged the author to rework the analysis of the nodal interpolation over intervals and present it in this extended and considerably revised form.) We show that, for arbitrary spaces of piecewise linear functions of one variable, the H 1-stability constant is bounded by one without any assumptions on the mesh sizes or on the relations between the meshes. We also give counterexamples for the nodal interpolation in higher order finite element spaces.

Suggested Citation

  • T. Dickopf, 2013. "Nodal Interpolation Between First-Order Finite Element Spaces in 1D is Uniformly H 1-Stable," Springer Books, in: Andrea Cangiani & Ruslan L. Davidchack & Emmanuil Georgoulis & Alexander N. Gorban & Jeremy Levesley (ed.), Numerical Mathematics and Advanced Applications 2011, edition 127, pages 419-427, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-33134-3_45
    DOI: 10.1007/978-3-642-33134-3_45
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:spr:sprchp:978-3-642-33134-3_45. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.