IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i12p1892-d1417386.html
   My bibliography  Save this article

Solution of the Elliptic Interface Problem by a Hybrid Mixed Finite Element Method

Author

Listed:
  • Yuhan Wang

    (School of Advanced Manufacturing, Guangdong University of Technology, Jieyang 522000, China)

  • Peiyao Wang

    (School of Advanced Manufacturing, Guangdong University of Technology, Jieyang 522000, China)

  • Rongpei Zhang

    (School of Advanced Manufacturing, Guangdong University of Technology, Jieyang 522000, China)

  • Jia Liu

    (School of Advanced Manufacturing, Guangdong University of Technology, Jieyang 522000, China)

Abstract

This paper addresses the elliptic interface problem involving jump conditions across the interface. We propose a hybrid mixed finite element method on the triangulation where the interfaces are aligned with the mesh. The second-order elliptic equation is initially decomposed into two equations by introducing a gradient term. Subsequently, weak formulations are applied to these equations. Scheme continuity is enforced using the Lagrange multiplier technique. Finally, we derive an explicit formula for the entries of the matrix equation representing Lagrange multiplier unknowns resulting from hybridization. The method yields approximations of all variables, including the solution and gradient, with optimal order. Furthermore, the matrix representing the final linear algebra systems is not only symmetric but also positive definite. Numerical examples convincingly demonstrate the effectiveness of the hybrid mixed finite element method in addressing elliptic interface problems.

Suggested Citation

  • Yuhan Wang & Peiyao Wang & Rongpei Zhang & Jia Liu, 2024. "Solution of the Elliptic Interface Problem by a Hybrid Mixed Finite Element Method," Mathematics, MDPI, vol. 12(12), pages 1-11, June.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:12:p:1892-:d:1417386
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/12/1892/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/12/1892/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Shi, Dongyang & Li, Minghao & Li, Zhenzhen, 2019. "A nonconforming finite element method for the stationary Smagorinsky model," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 308-319.
    Full references (including those not matched with items on IDEAS)

    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. Zheng, Bo & Shang, Yueqiang, 2022. "A two-step stabilized finite element algorithm for the Smagorinsky model," Applied Mathematics and Computation, Elsevier, vol. 422(C).

    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:12:p:1892-:d:1417386. 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: 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.