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

HASLINGER Jaroslav, KUČERA Radek, ŠÁTEK Václav and SASSI Taoufik. Stokes system with solution-dependent threshold slip boundary conditions: Analysis, approximation and implementation. Mathematics and Mechanics of Solids, vol. 2018, no. 23, pp. 294-307. ISSN 1081-2865. Available from: http://journals.sagepub.com/doi/full/10.1177/1081286517716222
Czech title
Stokesova úloha se závislým řešením na prahovém prokluzu: analýza, aproximace a implementace
Type
journal article
Language
english
Authors
Haslinger Jaroslav (CUNI)
Kučera Radek, prof. RNDr., Ph.D. (VŠB-TUO)
Šátek Václav, Ing., Ph.D. (DITS FIT BUT)
Sassi Taoufik, prof. (Université Caen Normandie)
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
Publisher
SAGE Publications
DOI
BibTeX
@ARTICLE{FITPUB11250,
   author = "Jaroslav Haslinger and Radek Ku\v{c}era and V\'{a}clav \v{S}\'{a}tek and Taoufik Sassi",
   title = "Stokes system with solution-dependent threshold slip boundary conditions: Analysis, approximation and implementation",
   pages = "294--307",
   journal = "Mathematics and Mechanics of Solids",
   volume = 2018,
   number = 23,
   year = 2018,
   ISSN = "1081-2865",
   doi = "10.1177/1081286517716222",
   language = "english",
   url = "https://www.fit.vut.cz/research/publication/11250"
}
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