IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v307y2017icp244-256.html
   My bibliography  Save this article

Galerkin finite element methods for convection–diffusion problems with exponential layers on Shishkin triangular meshes and hybrid meshes

Author

Listed:
  • Liu, Xiaowei
  • Zhang, Jin

Abstract

In this work, we provide a convergence analysis for a Galerkin finite element method on a Shishkin triangular mesh and a hybrid mesh for a singularly perturbed convection–diffusion equation. The hybrid mesh replaces the triangles of the Shishkin mesh by rectangles in the layer regions. The supercloseness results are established that the computed solution converges to the interpolant of the true solution with 3/2 order and 2 order (up to a logarithmic factor) on the two kinds of mesh, respectively. These convergence rates are uniformly valid with respect to the diffusion parameter and imply that the hybrid mesh is superior to the Shishkin triangular mesh. Numerical experiments illustrate these theoretical results.

Suggested Citation

  • Liu, Xiaowei & Zhang, Jin, 2017. "Galerkin finite element methods for convection–diffusion problems with exponential layers on Shishkin triangular meshes and hybrid meshes," Applied Mathematics and Computation, Elsevier, vol. 307(C), pages 244-256.
    • Handle: RePEc:eee:apmaco:v:307:y:2017:i:c:p:244-256
    DOI: 10.1016/j.amc.2017.03.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300317301741
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2017.03.003?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:apmaco:v:307:y:2017:i:c:p:244-256. 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.