IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-642-33134-3_44.html
   My bibliography  Save this book chapter

Coupling Hdiv an H1 Finite Element Approximations for a Poisson Problem

In: Numerical Mathematics and Advanced Applications 2011

Author

Listed:
  • D. de Siqueira

    (IMECC-Unicamp)

  • P. R. B. Devloo

    (FEC-Unicamp)

  • S. M. Gomes

    (IMECC-Unicamp)

Abstract

The purpose of the paper is to approximate an elliptic problem coupling two different formulations. The domain is split into two non-overlapping sub-domains. On the first one, the problem is approximated using classical Galerkin method where the primal solution p is searched in H 1 approximation spaces. On the other one, the mixed formulation is applied, which is based on Hdiv and L 2 approximation spaces for the dual ∇ p and primal p solutions, respectively. On the interface, the continuity of p and ∇ p is imposed strongly, using transmission conditions. The resulting coupled formulation is a saddle point problem, which is solved for high order hierarchical approximation spaces. Numerical simulations for a test problem show consistent rates of convergence when compared with the corresponding classical and mixed formulations in the whole domain.

Suggested Citation

  • D. de Siqueira & P. R. B. Devloo & S. M. Gomes, 2013. "Coupling Hdiv an H1 Finite Element Approximations for a Poisson Problem," 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 411-417, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-33134-3_44
    DOI: 10.1007/978-3-642-33134-3_44
    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_44. 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.