Publication Details
Dual strategies for solving the Stokes problem with stick-slip boundary conditions in 3D
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{BUT168554,
author="Jaroslav {Haslinger} and Radek {Kučera} and Taoufik {Sassi} and Václav {Šátek}",
title="Dual strategies for solving the Stokes problem with stick-slip boundary conditions in 3D",
journal="Mathematics and Computers in Simulation",
year="2021",
volume="2021",
number="189",
pages="191--206",
doi="10.1016/j.matcom.2020.12.015",
issn="0378-4754",
url="https://www.sciencedirect.com/science/article/pii/S0378475420304705"
}