IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v246y2026icp491-508.html

Supercloseness of weak Galerkin methods in a weighted and balanced norm for singularly perturbed reaction–diffusion problems

Author

Listed:
  • Toprakseven, Suayip
  • Zhu, Peng

Abstract

In this paper, we analyze the error of the weak Galerkin finite element method (WG-FEM) for singularly perturbed reaction–diffusion equations using piecewise discontinuous bilinear polynomials on a 2D Shishkin mesh. To accurately capture boundary layer effects, we introduce a weighted and balanced norm that is stronger than the standard energy norm. Unlike traditional approaches, which rely on global or local L2-projections and face challenges in 2D settings, our balanced norm is defined using a weight function together with the bilinear interpolation operator. By employing integral identities, we establish supercloseness results on Shishkin meshes. Numerical experiments confirm the sharpness of the theoretical analysis.

Suggested Citation

  • Toprakseven, Suayip & Zhu, Peng, 2026. "Supercloseness of weak Galerkin methods in a weighted and balanced norm for singularly perturbed reaction–diffusion problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 246(C), pages 491-508.
    • Handle: RePEc:eee:matcom:v:246:y:2026:i:c:p:491-508
    DOI: 10.1016/j.matcom.2026.02.019
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475426000650
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2026.02.019?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

    for a different version of it.

    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:eee:matcom:v:246:y:2026:i:c:p:491-508. 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.