Faculty of Information Technology, BUT

Publication Details

Efficient methods for solving the Stokes problem with slip boundary conditions

KUČERA Radek, HASLINGER Jaroslav, ŠÁTEK Václav and JAROŠOVÁ Marta. Efficient methods for solving the Stokes problem with slip boundary conditions. Mathematics and Computers in Simulation, vol. 2018, no. 145, pp. 114-124. ISSN 0378-4754. Available from: https://www.sciencedirect.com/science/article/abs/pii/S0378475416301215
Type
journal article
Language
english
Authors
Kučera Radek, prof. RNDr., Ph.D. (VŠB-TUO)
Haslinger Jaroslav (CUNI)
Šátek Václav, Ing., Ph.D. (DITS FIT BUT)
Jarošová Marta (VŠB-TUO)
URL
Keywords
Stokes problem, slip boundary condition, active-set algorithm,
interior-point method
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.
Published
2018
Pages
114-124
Journal
Mathematics and Computers in Simulation, vol. 2018, no. 145, ISSN 0378-4754
Book
IMACS - Mathematics and Computers in Simulation
DOI
BibTeX
@ARTICLE{FITPUB10865,
   author = "Radek Ku\v{c}era and Jaroslav Haslinger and V\'{a}clav \v{S}\'{a}tek and Marta Jaro\v{s}ov\'{a}",
   title = "Efficient methods for solving the Stokes problem with slip boundary conditions",
   pages = "114--124",
   booktitle = "IMACS - Mathematics and Computers in Simulation",
   journal = "Mathematics and Computers in Simulation",
   volume = 2018,
   number = 145,
   year = 2018,
   ISSN = "0378-4754",
   doi = "10.1016/j.matcom.2016.05.012",
   language = "english",
   url = "https://www.fit.vut.cz/research/publication/10865"
}
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