IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-0-8176-8394-8_4.html
   My bibliography  Save this book chapter

Space-Time Hybridizable Discontinuous Galerkin Method for the Advection–Diffusion Equation on Moving and Deforming Meshes

In: The Courant–Friedrichs–Lewy (CFL) Condition

Author

Listed:
  • Sander Rhebergen

    (University of Minnesota, School of Mathematics)

  • Bernardo Cockburn

    (University of Minnesota, School of Mathematics)

Abstract

We present the first space-time hybridizable discontinuous Galerkin finite element method for the advection–diffusion equation. Space-time discontinuous Galerkin methods have been proven to be very well suited for moving and deforming meshes which automatically satisfy the so-called Geometric Conservation law, for being able to provide higher-order accurate approximations in both time and space by simply increasing the degree of the polynomials used for the space-time finite elements, and for easily handling space-time adaptivity strategies. The hybridizable discontinuous Galerkin methods we introduce here add to these advantages their distinctive feature, namely, that the only globally-coupled degrees of freedom are those of the approximate trace of the scalar unknown. This results in a significant reduction of the size of the matrices to be numerically inverted, a more efficient implementation, and even better accuracy. We introduce the method, discuss its implementation and numerically explore its convergence properties.

Suggested Citation

  • Sander Rhebergen & Bernardo Cockburn, 2013. "Space-Time Hybridizable Discontinuous Galerkin Method for the Advection–Diffusion Equation on Moving and Deforming Meshes," Springer Books, in: Carlos A. de Moura & Carlos S. Kubrusly (ed.), The Courant–Friedrichs–Lewy (CFL) Condition, edition 127, pages 45-63, Springer.
    • Handle: RePEc:spr:sprchp:978-0-8176-8394-8_4
    DOI: 10.1007/978-0-8176-8394-8_4
    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:978-0-8176-8394-8_4. 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.