Publication result detail

Dual strategies for solving the Stokes problem with stick-slip boundary conditions in 3D

HASLINGER, J.; KUČERA, R.; SASSI, T.; ŠÁTEK, V.

Original Title

Dual strategies for solving the Stokes problem with stick-slip boundary conditions in 3D

English Title

Dual strategies for solving the Stokes problem with stick-slip boundary conditions in 3D

Type

WoS Article

Original Abstract

The paper deals with the numerical realization of the 3D Stokes flow subject to threshold slip boundary conditions. The
weak velocity-pressure formulation leads to an inequality type problem that is approximated by a mixed finite element method.
The resulting algebraic system is non-smooth. Besides the pressure, three additional Lagrange multipliers are introduced: the
discrete normal stress releasing the impermeability condition and two discrete shear stresses regularizing the non-smooth slip
term. Eliminating the discrete velocity component we obtain the minimization problem for the smooth functional, expressed
in terms of the pressure, the normal, and the shear stresses. This problem is solved either by a path following variant of the
interior point method or by the semi-smooth Newton method. Numerical scalability is illustrated by computational experiments.

English abstract

The paper deals with the numerical realization of the 3D Stokes flow subject to threshold slip boundary conditions. The
weak velocity-pressure formulation leads to an inequality type problem that is approximated by a mixed finite element method.
The resulting algebraic system is non-smooth. Besides the pressure, three additional Lagrange multipliers are introduced: the
discrete normal stress releasing the impermeability condition and two discrete shear stresses regularizing the non-smooth slip
term. Eliminating the discrete velocity component we obtain the minimization problem for the smooth functional, expressed
in terms of the pressure, the normal, and the shear stresses. This problem is solved either by a path following variant of the
interior point method or by the semi-smooth Newton method. Numerical scalability is illustrated by computational experiments.

Keywords

Stokes problem, Stick-slip boundary conditions, Interior-point method, Semi-smooth Newton method

Key words in English

Stokes problem, Stick-slip boundary conditions, Interior-point method, Semi-smooth Newton method

Authors

HASLINGER, J.; KUČERA, R.; SASSI, T.; ŠÁTEK, V.

RIV year

2022

Released

09.11.2021

ISBN

0378-4754

Periodical

MATHEMATICS AND COMPUTERS IN SIMULATION

Volume

2021

Number

189

State

Kingdom of the Netherlands

Pages from

191

Pages to

206

Pages count

16

URL

https://www.sciencedirect.com/science/article/pii/S0378475420304705

BibTex

@article{BUT168554,
  author="Jaroslav {Haslinger} and Radek {Kučera} and Taoufik {Sassi} and Václav {Šátek}",
  title="Dual strategies for solving the Stokes problem with stick-slip boundary conditions in 3D",
  journal="MATHEMATICS AND COMPUTERS IN SIMULATION",
  year="2021",
  volume="2021",
  number="189",
  pages="191--206",
  doi="10.1016/j.matcom.2020.12.015",
  issn="0378-4754",
  url="https://www.sciencedirect.com/science/article/pii/S0378475420304705"
}

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