IDEAS home Printed from https://ideas.repec.org/a/taf/nmcmxx/v17y2010i4p443-461.html
   My bibliography  Save this article

Reduced basis approximation and a posteriori error estimates for a multiscale liquid crystal model

Author

Listed:
  • David J. Knezevic

Abstract

We present a reduced basis framework and associated a posteriori error estimates for the multiscale Stokes Fokker--Planck system that governs the flow of a dilute suspension of rod-like molecules immersed in a Newtonian solvent, relevant in liquid crystals modelling. The Fokker--Planck equation dictates the microscale behaviour and must be solved at every quadrature point of the macroscale finite element mesh -- this is a natural example of a many-query problem for which the certified reduced basis method is well suited. We focus on a Poiseuille flow problem to simplify the presentation of ideas, but we note that the methods developed in this article generalize directly to more complicated problems. Numerical results demonstrate that our reduced basis approach leads to significant computational savings and also that our error estimator performs well for moderate parameter values.

Suggested Citation

  • David J. Knezevic, 2010. "Reduced basis approximation and a posteriori error estimates for a multiscale liquid crystal model," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 17(4), pages 443-461, June.
    • Handle: RePEc:taf:nmcmxx:v:17:y:2010:i:4:p:443-461
    DOI: 10.1080/13873954.2011.547676
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/13873954.2011.547676
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/13873954.2011.547676?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.

    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:443-461. 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.