Publication Details
Stokes problem with the Coulomb stick-slip boundary conditions in 3D: formulations, approximation, algorithms, and experiments
Kučera Radek, prof. RNDr., Ph.D.
Šátek Václav, Ing., Ph.D. (DITS)
Motyčková Kristina, Ing., Ph.D.
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{BUT185170,
author="Jaroslav {Haslinger} and Radek {Kučera} and Václav {Šátek} and Kristina {Motyčková}",
title="Stokes problem with the Coulomb stick-slip boundary conditions in 3D: formulations, approximation, algorithms, and experiments",
journal="Mathematics and Computers in Simulation",
year="2024",
volume="2024",
number="216",
pages="145--167",
doi="10.1016/j.matcom.2023.08.036",
issn="0378-4754",
url="https://www.sciencedirect.com/science/article/pii/S0378475423003737"
}