Publication Details
Stokes system with solution-dependent threshold slip boundary conditions: Analysis, approximation and implementation
Kučera Radek, prof. RNDr., Ph.D.
Šátek Václav, Ing., Ph.D. (DITS)
Sassi Taoufik (FIT)
Stokes system, threshold slip boundary conditions, solution dependent slip function
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.
@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"
}