Detail publikačního výsledku

Efficient methods for solving the Stokes problem with slip boundary conditions

KUČERA, R.; HASLINGER, J.; ŠÁTEK, V.; JAROŠOVÁ, M.

Originální název

Efficient methods for solving the Stokes problem with slip boundary conditions

Anglický název

Efficient methods for solving the Stokes problem with slip boundary conditions

Druh

Článek WoS

Originální abstrakt

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.

Anglický abstrakt

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.

Klíčová slova

Stokes problem, slip boundary condition, active-set algorithm,
interior-point method

Klíčová slova v angličtině

Stokes problem, slip boundary condition, active-set algorithm,
interior-point method

Autoři

KUČERA, R.; HASLINGER, J.; ŠÁTEK, V.; JAROŠOVÁ, M.

Vydáno

05.03.2018

Kniha

IMACS - Mathematics and Computers in Simulation

ISSN

0378-4754

Periodikum

MATHEMATICS AND COMPUTERS IN SIMULATION

Svazek

2018

Číslo

145

Stát

Nizozemsko

Strany od

114

Strany do

124

Strany počet

11

URL

https://www.sciencedirect.com/science/article/abs/pii/S0378475416301215

BibTex

@article{BUT168511,
  author="KUČERA, R. and HASLINGER, J. and ŠÁTEK, V. and JAROŠOVÁ, M.",
  title="Efficient methods for solving the Stokes problem with slip boundary conditions",
  journal="MATHEMATICS AND COMPUTERS IN SIMULATION",
  year="2018",
  volume="2018",
  number="145",
  pages="114--124",
  doi="10.1016/j.matcom.2016.05.012",
  issn="0378-4754",
  url="https://www.sciencedirect.com/science/article/abs/pii/S0378475416301215"
}