IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v431y2022ics0096300322003897.html
   My bibliography  Save this article

Analysis of finite element method in balanced norms for two-parameter singularly perturbed problems

Author

Listed:
  • Lv, Yanhui
  • Zhang, Jin

Abstract

We consider the two-parameter singularly perturbed problems, and there are two exponential boundary layers in its solution. In general, the energy norm is used in error estimations of finite element method for singularly perturbed problems. However, it is difficult to capture each layer simultaneously in this norm. In this paper, a special balanced norm is defined, which can capture each exponential layer well. Based on the balanced norm, we obtain the uniform convergence of any order finite element method with respect to both parameters on a Shishkin mesh. Moreover, the optimal order is proved and some discussions in this balanced norm are presented. Finally, we give some numerical examples to verify our theoretical findings.

Suggested Citation

  • Lv, Yanhui & Zhang, Jin, 2022. "Analysis of finite element method in balanced norms for two-parameter singularly perturbed problems," Applied Mathematics and Computation, Elsevier, vol. 431(C).
    • Handle: RePEc:eee:apmaco:v:431:y:2022:i:c:s0096300322003897
    DOI: 10.1016/j.amc.2022.127315
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300322003897
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2022.127315?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.

    References listed on IDEAS

    as
    1. Zhang, Jin & Lv, Yanhui, 2021. "High-order finite element method on a Bakhvalov-type mesh for a singularly perturbed convection–diffusion problem with two parameters," Applied Mathematics and Computation, Elsevier, vol. 397(C).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ma, Xiaoqi & Zhang, Jin, 2023. "Supercloseness in a balanced norm of the NIPG method on Shishkin mesh for a reaction diffusion problem," Applied Mathematics and Computation, Elsevier, vol. 444(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lv, Yanhui & Zhang, Jin, 2022. "Convergence and supercloseness of a finite element method for a two-parameter singularly perturbed problem on Shishkin triangular mesh," Applied Mathematics and Computation, Elsevier, vol. 416(C).
    2. Zhang, Jin & Liu, Xiaowei, 2022. "Uniform convergence of a weak Galerkin method for singularly perturbed convection–diffusion problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 393-403.

    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:431:y:2022:i:c:s0096300322003897. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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.