IDEAS home Printed from https://ideas.repec.org/a/spr/pardea/v1y2020i4d10.1007_s42985-020-00020-4.html
   My bibliography  Save this article

Structure aware Runge–Kutta time stepping for spacetime tents

Author

Listed:
  • Jay Gopalakrishnan

    (Portland State University)

  • Joachim Schöberl

    (Technische Universität Wien)

  • Christoph Wintersteiger

    (Technische Universität Wien)

Abstract

We introduce a new class of Runge–Kutta type methods suitable for time stepping to propagate hyperbolic solutions within tent-shaped spacetime regions. Unlike standard Runge–Kutta methods, the new methods yield expected convergence properties when standard high order spatial (discontinuous Galerkin) discretizations are used. After presenting a derivation of nonstandard order conditions for these methods, we show numerical examples of nonlinear hyperbolic systems to demonstrate the optimal convergence rates. We also report on the discrete stability properties of these methods applied to linear hyperbolic equations.

Suggested Citation

  • Jay Gopalakrishnan & Joachim Schöberl & Christoph Wintersteiger, 2020. "Structure aware Runge–Kutta time stepping for spacetime tents," Partial Differential Equations and Applications, Springer, vol. 1(4), pages 1-24, August.
    • Handle: RePEc:spr:pardea:v:1:y:2020:i:4:d:10.1007_s42985-020-00020-4
    DOI: 10.1007/s42985-020-00020-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s42985-020-00020-4
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s42985-020-00020-4?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.

    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:pardea:v:1:y:2020:i:4:d:10.1007_s42985-020-00020-4. 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.