IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v145y2018icp114-124.html
   My bibliography  Save this article

Efficient methods for solving the Stokes problem with slip boundary conditions

Author

Listed:
  • Kučera, Radek
  • Haslinger, Jaroslav
  • Šátek, Václav
  • Jarošová, Marta

Abstract

The paper deals with the Stokes flow with the threshold slip boundary conditions. A finite element approximation of the problem leads to the minimization of a non-differentiable energy functional subject to two linear equality constraints: the impermeability condition on the slip part of the boundary and the incompressibility of the fluid. Eliminating the velocity components, one gets the smooth dual functional in terms of three Lagrange multipliers. The first Lagrange multiplier regularizes the problem. Its components are subject to simple bounds. The other two Lagrange multipliers treat the impermeability and the incompressibility conditions. The last Lagrange multiplier represents the pressure in the whole domain. The solution to the dual problem is computed by an active set strategy and a path-following variant of the interior-point method. Numerical experiments illustrate computational efficiency.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:145:y:2018:i:c:p:114-124
    DOI: 10.1016/j.matcom.2016.05.012
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475416301215
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2016.05.012?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.

    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.
    2. 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.

    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:145:y:2018:i:c:p:114-124. 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: 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.