IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v273y2016icp842-855.html
   My bibliography  Save this article

A new nonconforming mixed finite element scheme for second order eigenvalue problem

Author

Listed:
  • Shi, Dongyang
  • Wang, Lele
  • Liao, Xin

Abstract

A new nonconforming mixed finite element method (MFEM for short) is established for the Laplace eigenvalue problem. Firstly, the optimal order error estimates for both the eigenvalue and eigenpair (the original variable u and the auxiliary variable p→=∇u) are deduced, the lower bound of eigenvalue is estimated simultaneously. Then, by use of the special property of the nonconforming EQ1rot element (the consistency error is of order O(h2) in broken H1-norm, which is one order higher than its interpolation error), the techniques of integral identity and interpolation postprocessing, we derive the superclose and superconvergence results of order O(h2) for u in broken H1-norm and p→ in L2-norm. Furthermore, with the help of asymptotic expansions, the extrapolation solution of order O(h3) for eigenvalue is obtained. Finally, some numerical results are presented to validate our theoretical analysis.

Suggested Citation

  • Shi, Dongyang & Wang, Lele & Liao, Xin, 2016. "A new nonconforming mixed finite element scheme for second order eigenvalue problem," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 842-855.
    • Handle: RePEc:eee:apmaco:v:273:y:2016:i:c:p:842-855
    DOI: 10.1016/j.amc.2015.10.064
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300315014150
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2015.10.064?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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Shi, Xiangyu & Lu, Linzhang, 2020. "A new two-grid nonconforming mixed finite element method for nonlinear Benjamin-Bona-Mahoney equation," Applied Mathematics and Computation, Elsevier, vol. 371(C).

    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:apmaco:v:273:y:2016:i:c:p:842-855. 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: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.