Publication Details
Dual strategies for solving the Stokes problem with stick-slip boundary conditions in 3D
Kučera Radek, prof. RNDr., Ph.D. (VŠB-TUO)
Sassi Taoufik, prof. (University of Caen Normandy)
Šátek Václav, Ing., Ph.D. (DITS FIT BUT)
Stokes problem, Stick-slip boundary conditions, Interior-point method, Semi-smooth Newton method
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.
@ARTICLE{FITPUB12442,
author = "Jaroslav Haslinger and Radek Ku\v{c}era and Taoufik Sassi and V\'{a}clav \v{S}\'{a}tek",
title = "Dual strategies for solving the Stokes problem with stick-slip boundary conditions in 3D",
pages = "191--206",
journal = "Mathematics and Computers in Simulation",
volume = 2021,
number = 189,
year = 2021,
ISSN = "0378-4754",
doi = "10.1016/j.matcom.2020.12.015",
language = "english",
url = "https://www.fit.vut.cz/research/publication/12442"
}