IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v496y2025ics0096300325000827.html
   My bibliography  Save this article

An α-robust two-grid finite element method with nonuniform L2-1σ scheme for the semilinear Caputo-Hadamard time-fractional diffusion equations involving initial singularity

Author

Listed:
  • Zeng, Yunhua
  • Tan, Zhijun

Abstract

Considering the initial singularity, a fully discrete two-grid finite element method (FEM) on nonuniform temporal meshes is constructed for the semilinear time-fractional variable coefficient diffusion equations (TF-VCDEs) with Caputo-Hadamard derivative. The nonuniform Llog⁡,2−1σ formula and two-grid method are employed to discretize the time and space directions, respectively. Through strict theoretical proof, the α-robust stability and optimal L2-norm and H1-norm error analysis for the fully discrete FEM and the two-grid method are obtained, where the error bound does not blow up as α→1−. To reduce computational costs, a fast two-grid method is constructed by approximating the kernel function with an effective sum-of-exponentials (SOE) technique. Finally, the accuracy and effectiveness of the two-grid method and its associated fast algorithm are verified through two numerical examples.

Suggested Citation

  • Zeng, Yunhua & Tan, Zhijun, 2025. "An α-robust two-grid finite element method with nonuniform L2-1σ scheme for the semilinear Caputo-Hadamard time-fractional diffusion equations involving initial singularity," Applied Mathematics and Computation, Elsevier, vol. 496(C).
    • Handle: RePEc:eee:apmaco:v:496:y:2025:i:c:s0096300325000827
    DOI: 10.1016/j.amc.2025.129355
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300325000827
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2025.129355?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:496:y:2025:i:c:s0096300325000827. 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.