IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-540-34288-5_8.html
   My bibliography  Save this book chapter

Functional Approach to Locally Based A Posteriori Error Estimates for Elliptic and Parabolic Problems

In: Numerical Mathematics and Advanced Applications

Author

Listed:
  • Sergey Repin

    (Russian Academy of Sciences, St. Petersburg Division of the Steklov Mathematical Institute)

Abstract

The paper is concerned with functional approach to the a posteriori error control for approximate solutions of differential equations. Functional a posteriori estimates are derived by purely functional methods using the analysis of variational problems or integral identities. They are intended to give computable minorants and majorants for various measures of the difference between exact solutions and their conforming approximations. Functional estimates contain no mesh dependent constants and provide guaranteed lower and upper bounds of errors. In this paper, the major attention is paid on a posteriori estimates in terms of local norms or locally based linear functionals. It is shown that for linear elliptic and parabolic problems functional estimates in global (energy) norms imply a posteriori estimates in terms of local quantities.

Suggested Citation

  • Sergey Repin, 2006. "Functional Approach to Locally Based A Posteriori Error Estimates for Elliptic and Parabolic Problems," Springer Books, in: Alfredo Bermúdez de Castro & Dolores Gómez & Peregrina Quintela & Pilar Salgado (ed.), Numerical Mathematics and Advanced Applications, pages 135-150, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-34288-5_8
    DOI: 10.1007/978-3-540-34288-5_8
    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

    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:978-3-540-34288-5_8. 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.