IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-662-43799-5_23.html
   My bibliography  Save this book chapter

High-Precision Eigenvalue Bound for the Laplacian with Singularities

In: Computer Mathematics

Author

Listed:
  • Xuefeng Liu

    (Waseda University, Research Institute for Science and Engineering)

  • Tomoaki Okayama

    (Hitotsubashi University, Graduate School of Economics)

  • Shin’ichi Oishi

    (Waseda University, Faculty of Science and Engineering
    CREST/JST)

Abstract

For the purpose of bounding eigenvalues of the Laplacian over a bounded polygonal domain, we propose an algorithm to give high-precision bound even in the case that the eigenfunction has singularities around reentrant corners. The algorithm is a combination of the finite element method and the Lehmann–Goerisch theorem. The interval arithmetic is adopted in floating point number computation. Since all the error in the computation, e.g., the function approximation error, the floating point number rounding error, are exactly estimated, the result can be mathematically correct. In the end of the chapter, there are computational examples over an L-shaped domain and a square-minus-square domain that demonstrate the efficiency of our proposed algorithm.

Suggested Citation

  • Xuefeng Liu & Tomoaki Okayama & Shin’ichi Oishi, 2014. "High-Precision Eigenvalue Bound for the Laplacian with Singularities," Springer Books, in: Ruyong Feng & Wen-shin Lee & Yosuke Sato (ed.), Computer Mathematics, edition 127, pages 311-323, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-43799-5_23
    DOI: 10.1007/978-3-662-43799-5_23
    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

    Keywords

    ;
    ;
    ;
    ;
    ;

    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:978-3-662-43799-5_23. 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.