IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v81y2011i9p1869-1875.html
   My bibliography  Save this article

On an approach to deal with Neumann boundary value problems defined on uncertain domains: Numerical experiments

Author

Listed:
  • Chleboun, Jan

Abstract

Neumann boundary value problems for second order elliptic equations are considered on a 2D domain whose boundary is not known and might be even non-Lipschitz. Although the domain of definition is unknown, it is assumed that (a) it contains a known domain (subdomain), (b) it is contained in a known domain (superdomain), and (c) both the subdomain and superdomain have Lipschitz boundary. To cope with the Neumann boundary condition on the unknown boundary and to properly formulate the boundary value problem (BVP), the condition has to be reformulated. A reformulated BVP is used to estimate the difference between the BVP solution on the unknown domain and the BVP solution on the known subdomain or superdomain. To evaluate the estimate, the finite element method is applied. Numerical experiments are performed to check the estimate and its response to a shrinking region of uncertainty.

Suggested Citation

  • Chleboun, Jan, 2011. "On an approach to deal with Neumann boundary value problems defined on uncertain domains: Numerical experiments," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(9), pages 1869-1875.
    • Handle: RePEc:eee:matcom:v:81:y:2011:i:9:p:1869-1875
    DOI: 10.1016/j.matcom.2011.02.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475411000759
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2011.02.005?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:eee:matcom:v:81:y:2011:i:9:p:1869-1875. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.