IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v178y2020icp464-484.html
   My bibliography  Save this article

Local and parallel stabilized finite element algorithms based on the lowest equal-order elements for the steady Navier–Stokes equations

Author

Listed:
  • Zheng, Bo
  • Shang, Yueqiang

Abstract

Based on a fully overlapping domain decomposition approach, local and parallel stabilized finite element algorithms are proposed and investigated for the steady incompressible Navier–Stokes equations, where the inf−sup unstable lowest equal-order P1−P1 finite element pairs are used and the stabilized term is based on two local Gauss integrations defined by the difference between a consistent and under-integrated matrix of pressure interpolants. In these algorithms, each processor computes a local stabilized solution in its own subdomain using a global grid that is locally refined around its own subdomain, making the algorithms have low communication cost and easy to implement based on a sequential solver. Using the technical tool of the local a priori estimate for the stabilized solution, error bounds of the proposed algorithms are derived. Theoretical and numerical results show that, the algorithms can yield an approximate solution with an accuracy comparable to that of the standard stabilized finite element solution with a substantial decrease in CPU time.

Suggested Citation

  • Zheng, Bo & Shang, Yueqiang, 2020. "Local and parallel stabilized finite element algorithms based on the lowest equal-order elements for the steady Navier–Stokes equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 464-484.
    • Handle: RePEc:eee:matcom:v:178:y:2020:i:c:p:464-484
    DOI: 10.1016/j.matcom.2020.07.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037847542030238X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2020.07.010?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. Zheng, Bo & Shang, Yueqiang, 2019. "Parallel iterative stabilized finite element algorithms based on the lowest equal-order elements for the stationary Navier–Stokes equations," Applied Mathematics and Computation, Elsevier, vol. 357(C), pages 35-56.
    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. Zheng, Bo & Shang, Yueqiang, 2022. "A two-step stabilized finite element algorithm for the Smagorinsky model," Applied Mathematics and Computation, Elsevier, vol. 422(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. Zheng, Bo & Shang, Yueqiang, 2020. "A two-level stabilized quadratic equal-order finite element variational multiscale method for incompressible flows," Applied Mathematics and Computation, Elsevier, vol. 384(C).
    2. 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:eee:matcom:v:178:y:2020:i:c:p:464-484. 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: 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.