Publication result detail

Stokes system with solution-dependent threshold slip boundary conditions: Analysis, approximation and implementation

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

Original Title

Stokes system with solution-dependent threshold slip boundary conditions: Analysis, approximation and implementation

English Title

Stokes system with solution-dependent threshold slip boundary conditions: Analysis, approximation and implementation

Type

WoS Article

Original Abstract

The paper analyzes the Stokes system with threshold slip boundary conditions of Navier type. Based on the fixedpoint
formulation we prove the existence of a solution for a class of solution-dependent slip functions g satisfying an
appropriate growth condition and its uniqueness provided that g is one-sided Lipschitz continuous. Further we study
under which conditions the respective fixed-point mapping is contractive. To discretize the problem we use P1-bubble/P1
elements. Properties of discrete models in dependence on the discretization parameter are analysed and convergence
results are established. In the second part of the paper we briefly describe the duality approach used in computations
and present results of a model example.

English abstract

The paper analyzes the Stokes system with threshold slip boundary conditions of Navier type. Based on the fixedpoint
formulation we prove the existence of a solution for a class of solution-dependent slip functions g satisfying an
appropriate growth condition and its uniqueness provided that g is one-sided Lipschitz continuous. Further we study
under which conditions the respective fixed-point mapping is contractive. To discretize the problem we use P1-bubble/P1
elements. Properties of discrete models in dependence on the discretization parameter are analysed and convergence
results are established. In the second part of the paper we briefly describe the duality approach used in computations
and present results of a model example.

Keywords

Stokes system, threshold slip boundary conditions, solution dependent slip function

Key words in English

Stokes system, threshold slip boundary conditions, solution dependent slip function

Authors

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

RIV year

2019

Released

01.03.2018

ISBN

1081-2865

Periodical

MATHEMATICS AND MECHANICS OF SOLIDS

Volume

2018

Number

23

State

United Kingdom of Great Britain and Northern Ireland

Pages from

294

Pages to

307

Pages count

14

URL

http://journals.sagepub.com/doi/full/10.1177/1081286517716222

BibTex

@article{BUT146571,
  author="Jaroslav {Haslinger} and Radek {Kučera} and Václav {Šátek} and Taoufik {Sassi}",
  title="Stokes system with solution-dependent threshold slip boundary conditions: Analysis, approximation and implementation",
  journal="MATHEMATICS AND MECHANICS OF SOLIDS",
  year="2018",
  volume="2018",
  number="23",
  pages="294--307",
  doi="10.1177/1081286517716222",
  issn="1081-2865",
  url="http://journals.sagepub.com/doi/full/10.1177/1081286517716222"
}