IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v223y2024icp171-182.html
   My bibliography  Save this article

High-order energy stable variable-step schemes for the time-fractional Cahn–Hilliard model

Author

Listed:
  • Zhang, Haiqing
  • Liao, Hong-lin

Abstract

Based on the Alikhanov formula of the Caputo derivative and the exponential scalar auxiliary variable approach, two different second-order stable numerical schemes are constructed for the time-fractional Cahn–Hilliard model, including the nonlinear L2-1σ scheme and the linear L2-1σ-ESAV scheme. Applying the discrete gradient structure, we construct the asymptotically compatible energies and the associated energy dissipation laws of these two schemes for the time-fractional Cahn–Hilliard model. Several experiments are carried out to demonstrate the accuracy of our schemes and compare their computational efficiency, as well as to investigate the coarsening dynamics of the time-fractional Cahn–Hilliard model with different adaptive time-stepping strategies. In the long-time simulations, the linear L2-1σ-ESAV scheme may be more costly than the nonlinear L2-1σ scheme although the linear scheme may take less time at each time level. It is observed that the energy of the L2-1σ-ESAV scheme prones to produce small fluctuations when large time steps are used.

Suggested Citation

  • Zhang, Haiqing & Liao, Hong-lin, 2024. "High-order energy stable variable-step schemes for the time-fractional Cahn–Hilliard model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 223(C), pages 171-182.
    • Handle: RePEc:eee:matcom:v:223:y:2024:i:c:p:171-182
    DOI: 10.1016/j.matcom.2024.04.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475424001319
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2024.04.005?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:matcom:v:223:y:2024:i:c:p:171-182. 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.