Publication result detail

Efficient methods for solving the Stokes problem with slip boundary conditions

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

Original Title

Efficient methods for solving the Stokes problem with slip boundary conditions

English Title

Efficient methods for solving the Stokes problem with slip boundary conditions

Type

WoS Article

Original 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.

English 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.

Keywords

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

Key words in English

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

Authors

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

Released

05.03.2018

Book

IMACS - Mathematics and Computers in Simulation

ISBN

0378-4754

Periodical

MATHEMATICS AND COMPUTERS IN SIMULATION

Volume

2018

Number

145

State

Kingdom of the Netherlands

Pages from

114

Pages to

124

Pages count

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"
}