IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-642-11795-4_46.html
   My bibliography  Save this book chapter

Finite Element Based Second Moment Analysis for Elliptic Problems in Stochastic Domains

In: Numerical Mathematics and Advanced Applications 2009

Author

Listed:
  • H. Harbrecht

    (University of Stuttgart, Institute for Applied Analysis and Numerical Simulation)

Abstract

We present a finite element method for the numerical solution of elliptic boundary value problems on stochastic domains. The method computes the mean and the variance of the random solution with leading order in the amplitude of the stochastic boundary perturbation relative to an unperturbed, nominal domain. The variance is computed as the trace of the solution’s two-point correlation which satisfies a deterministic boundary value problem on the tensor product of the nominal domain. This problem is discretized in the sparse tensor product space by a multilevel frame generated from standard finite elements. The computational complexity of the resulting approach stays essentially proportional to the number of finite elements required for the discretization of the nominal domain.

Suggested Citation

  • H. Harbrecht, 2010. "Finite Element Based Second Moment Analysis for Elliptic Problems in Stochastic Domains," Springer Books, in: Gunilla Kreiss & Per Lötstedt & Axel Målqvist & Maya Neytcheva (ed.), Numerical Mathematics and Advanced Applications 2009, pages 433-441, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-11795-4_46
    DOI: 10.1007/978-3-642-11795-4_46
    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

    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:978-3-642-11795-4_46. 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.