IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v189y2021icp191-206.html
   My bibliography  Save this article

Dual strategies for solving the Stokes problem with stick–slip boundary conditions in 3D

Author

Listed:
  • Haslinger, Jaroslav
  • Kučera, Radek
  • Sassi, Taoufik
  • Šátek, Václav

Abstract

The paper deals with the numerical realization of the 3D Stokes flow subject to threshold slip boundary conditions. The weak velocity–pressure formulation leads to an inequality type problem that is approximated by a mixed finite element method. The resulting algebraic system is non-smooth. Besides the pressure, three additional Lagrange multipliers are introduced: the discrete normal stress releasing the impermeability condition and two discrete shear stresses regularizing the non-smooth slip term. Eliminating the discrete velocity component we obtain the minimization problem for the smooth functional, expressed in terms of the pressure, the normal, and the shear stresses. This problem is solved either by a path following variant of the interior point method or by the semi-smooth Newton method. Numerical scalability is illustrated by computational experiments.

Suggested Citation

  • Haslinger, Jaroslav & Kučera, Radek & Sassi, Taoufik & Šátek, Václav, 2021. "Dual strategies for solving the Stokes problem with stick–slip boundary conditions in 3D," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 189(C), pages 191-206.
    • Handle: RePEc:eee:matcom:v:189:y:2021:i:c:p:191-206
    DOI: 10.1016/j.matcom.2020.12.015
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475420304705
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2020.12.015?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. Kučera, Radek & Haslinger, Jaroslav & Šátek, Václav & Jarošová, Marta, 2018. "Efficient methods for solving the Stokes problem with slip boundary conditions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 145(C), pages 114-124.
    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. Jaroslav Haslinger & Radek Kučera & Kristina Motyčková & Václav Šátek, 2021. "Numerical Modeling of the Leak through Semipermeable Walls for 2D/3D Stokes Flow: Experimental Scalability of Dual Algorithms," Mathematics, MDPI, vol. 9(22), pages 1-24, November.

    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. Jaroslav Haslinger & Radek Kučera & Kristina Motyčková & Václav Šátek, 2021. "Numerical Modeling of the Leak through Semipermeable Walls for 2D/3D Stokes Flow: Experimental Scalability of Dual Algorithms," Mathematics, MDPI, vol. 9(22), pages 1-24, November.

    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:189:y:2021:i:c:p:191-206. 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.