Journal article

KUČERA Radek, HASLINGER Jaroslav, ©ÁTEK Václav and JARO©OVÁ Marta. Efficient methods for solving the Stokes problem with slip boundary conditions. Mathematics and Computers in Simulation. 2018, vol. 2018, no. 145, pp. 114-124. ISSN 0378-4754. Available from:
Publication language:english
Original title:Efficient methods for solving the Stokes problem with slip boundary conditions
Book:IMACS - Mathematics and Computers in Simulation
Journal:Mathematics and Computers in Simulation, Vol. 2018, No. 145, US
Stokes problem, slip boundary condition, active-set algorithm,
interior-point method
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.
   author = {Radek Ku{\v{c}}era and Jaroslav Haslinger and
	V{\'{a}}clav {\v{S}}{\'{a}}tek and Marta
   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 = {}

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