IDEAS home Printed from https://ideas.repec.org/a/taf/nmcmxx/v17y2010i4p395-422.html
   My bibliography  Save this article

An hp certified reduced basis method for parametrized parabolic partial differential equations

Author

Listed:
  • Jens L. Eftang
  • David J. Knezevic
  • Anthony T. Patera

Abstract

In this article, we introduce an hp certified reduced basis (RB) method for parabolic partial differential equations. We invoke a Proper Orthogonal Decomposition (POD) (in time)/Greedy (in parameter) sampling procedure first in the initial partition of the parameter domain ( h -refinement) and subsequently in the construction of RB approximation spaces restricted to each parameter subdomain ( p -refinement). We show that proper balance between additional POD modes and additional parameter values in the initial subdivision process guarantees convergence of the approach. We present numerical results for two model problems: linear convection--diffusion and quadratically non-linear Boussinesq natural convection. The new procedure is significantly faster (more costly) in the RB Online (Offline) stage.

Suggested Citation

  • Jens L. Eftang & David J. Knezevic & Anthony T. Patera, 2010. "An hp certified reduced basis method for parametrized parabolic partial differential equations," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 17(4), pages 395-422, September.
    • Handle: RePEc:taf:nmcmxx:v:17:y:2010:i:4:p:395-422
    DOI: 10.1080/13873954.2011.547670
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/13873954.2011.547670
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/13873954.2011.547670?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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. M. Redeker & B. Haasdonk, 2016. "A POD–EIM reduced two-scale model for precipitation in porous media," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 22(4), pages 323-344, July.

    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:taf:nmcmxx:v:17:y:2010:i:4:p:395-422. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/NMCM20 .

    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.