Publication Details

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

HASLINGER, J.; KUČERA, R.; ŠÁTEK, V.; SASSI, T. Stokes system with solution-dependent threshold slip boundary conditions: Analysis, approximation and implementation. MATHEMATICS AND MECHANICS OF SOLIDS, 2018, vol. 2018, no. 23, p. 294-307. ISSN: 1081-2865.
Czech title
Stokesova úloha se závislým řešením na prahovém prokluzu: analýza, aproximace a implementace
Type
journal article
Language
English
Authors
Haslinger Jaroslav
Kučera Radek, prof. RNDr., Ph.D.
Šátek Václav, Ing., Ph.D. (DITS)
Sassi Taoufik (FIT)
URL
Keywords

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

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.

Published
2018
Pages
294–307
Journal
MATHEMATICS AND MECHANICS OF SOLIDS, vol. 2018, no. 23, ISSN 1081-2865
DOI
UT WoS
000429895300004
EID Scopus
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"
}
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