IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i17p2610-d1462683.html
   My bibliography  Save this article

Robust a Posteriori Error Estimates of Time-Dependent Poisson–Nernst–Planck Equations

Author

Listed:
  • Keli Fu

    (School of Mathematical Sciences, East China Normal University, Shanghai 200241, China)

  • Tingting Hao

    (Hua Lookeng Honors College, Changzhou University, Changzhou 213164, China)

Abstract

The paper considers the a posteriori error estimates for fully discrete approximations of time-dependent Poisson–Nernst–Planck (PNP) equations, which provide tools that allow for optimizing the choice of each time step when working with adaptive meshes. The equations are discretized by the Backward Euler scheme in time and conforming finite elements in space. Overcoming the coupling of time and the space with a full discrete solution and dealing with nonlinearity by taking G-derivatives of the nonlinear system, the computable, robust, effective, and reliable space–time a posteriori error estimation is obtained. The adaptive algorithm constructed based on the estimates realizes the parallel adaptations of time steps and mesh refinements, which are verified by numerical experiments with the time singular point and adaptive mesh refinement with boundary layer effects.

Suggested Citation

  • Keli Fu & Tingting Hao, 2024. "Robust a Posteriori Error Estimates of Time-Dependent Poisson–Nernst–Planck Equations," Mathematics, MDPI, vol. 12(17), pages 1-27, August.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:17:p:2610-:d:1462683
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/17/2610/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/17/2610/
    Download Restriction: no
    ---><---

    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:gam:jmathe:v:12:y:2024:i:17:p:2610-:d:1462683. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.