Publication Details
Stokes problem with the Coulomb stick-slip boundary conditions in 3D: formulations, approximation, algorithms, and experiments
Kučera Radek, prof. RNDr., Ph.D. (VŠB-TUO)
Motyčková Kristina, Mgr., Ph.D. (VŠB-TUO)
Šátek Václav, Ing., Ph.D. (DITS FIT BUT)
Stokes problem, Coulomb stick-slip boundary conditions, successive approximations, semi-smooth Newton method
The paper deals with the approximation and numerical realization of the Stokes system in 3D with Coulomb's slip boundary conditions. The weak velocity-pressure formulation leads to an implicit in- equality type problem which is discretized by the P1+bubble/P1 elements. To regularize the discrete non-smooth slip term and to release the discrete impermeability condition the duality approach is used. For numerical realization of the resulting saddle-point problem two strategies are proposed, namely i) its fixed-point formulation solved by the method of successive approximations ii) the direct numerical solu- tion of the saddle-point problem. The semi-smooth Newton method is used to solve non-smooth equations appearing in both these approaches.
@ARTICLE{FITPUB13003,
author = "Jaroslav Haslinger and Radek Ku\v{c}era and Kristina Moty\v{c}kov\'{a} and V\'{a}clav \v{S}\'{a}tek",
title = "Stokes problem with the Coulomb stick-slip boundary conditions in 3D: formulations, approximation, algorithms, and experiments",
pages = "145--167",
journal = "Mathematics and Computers in Simulation",
volume = 2024,
number = 216,
year = 2024,
ISSN = "0378-4754",
doi = "10.1016/j.matcom.2023.08.036",
language = "english",
url = "https://www.fit.vut.cz/research/publication/13003"
}