IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v2y2014i4p196-217d40691.html
   My bibliography  Save this article

The Second-Order Shape Derivative of Kohn–Vogelius-Type Cost Functional Using the Boundary Differentiation Approach

Author

Listed:
  • Jerico B. Bacani

    (Department of Mathematics and Computer Science, College of Science, University of the Philippines Baguio, Governor Pack Road, Baguio 2600, Philippines)

  • Gunther Peichl

    (Institute for Mathematics and Scientific Computing, University of Graz, Heinrichstrasse 36, A-8010 Graz, Austria)

Abstract

A shape optimization method is used to study the exterior Bernoulli free boundaryproblem. We minimize the Kohn–Vogelius-type cost functional over a class of admissibledomains subject to two boundary value problems. The first-order shape derivative of the costfunctional is recalled and its second-order shape derivative for general domains is computedvia the boundary differentiation scheme. Additionally, the second-order shape derivative ofJ at the solution of the Bernoulli problem is computed using Tiihonen’s approach.

Suggested Citation

  • Jerico B. Bacani & Gunther Peichl, 2014. "The Second-Order Shape Derivative of Kohn–Vogelius-Type Cost Functional Using the Boundary Differentiation Approach," Mathematics, MDPI, vol. 2(4), pages 1-22, September.
    • Handle: RePEc:gam:jmathe:v:2:y:2014:i:4:p:196-217:d:40691
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/2/4/196/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/2/4/196/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jerico B. Bacani & Gunther Peichl, 2013. "On the First-Order Shape Derivative of the Kohn-Vogelius Cost Functional of the Bernoulli Problem," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-19, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.

      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:gam:jmathe:v:2:y:2014:i:4:p:196-217:d:40691. 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.

      If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.