Journal articleKUČERA Radek, HASLINGER Jaroslav, ©ÁTEK Václav and JARO©OVÁ Marta. Efficient methods for solving the Stokes problem with slip boundary conditions. Mathematics and Computers in Simulation. 2018, vol. 2018, no. 145, pp. 114124. ISSN 03784754. Available from: https://www.sciencedirect.com/science/article/abs/pii/S0378475416301215  Publication language:  english 

Original title:  Efficient methods for solving the Stokes problem with slip boundary conditions 

Pages:  114124 

Book:  IMACS  Mathematics and Computers in Simulation 

Place:  US 

Year:  2018 

URL:  https://www.sciencedirect.com/science/article/abs/pii/S0378475416301215 

Journal:  Mathematics and Computers in Simulation, Vol. 2018, No. 145, US 

ISSN:  03784754 

DOI:  10.1016/j.matcom.2016.05.012 

Keywords 

Stokes problem, slip boundary condition, activeset algorithm, interiorpoint method 
Annotation 

The paper deals with the Stokes flow with the threshold slip boundary conditions. A finite element approximation of the problem leads to the minimization of a nondifferentiable energy functional subject to two linear equality constraints: the impermeability condition on the slip part of the boundary and the incompressibility of the fluid. Eliminating the velocity components, one gets the smooth dual functional in terms of three Lagrange multipliers. The first Lagrange multiplier regularizes the problem. Its components are subject to simple bounds. The other two Lagrange multipliers treat the impermeability and the incompressibility conditions. The last Lagrange multiplier represents the pressure in the whole domain. The solution to the dual problem is computed by an active set strategy and a pathfollowing variant of the interiorpoint method. Numerical experiments illustrate computational efficiency.

BibTeX: 

@ARTICLE{
author = {Radek Ku{\v{c}}era and Jaroslav Haslinger and
V{\'{a}}clav {\v{S}}{\'{a}}tek and Marta
Jaro{\v{s}}ov{\'{a}}},
title = {Efficient methods for solving the Stokes problem
with slip boundary conditions},
pages = {114124},
booktitle = {IMACS  Mathematics and Computers in Simulation},
journal = {Mathematics and Computers in Simulation},
volume = {2018},
number = {145},
year = {2018},
ISSN = {03784754},
doi = {10.1016/j.matcom.2016.05.012},
language = {english},
url = {http://www.fit.vutbr.cz/research/view_pub.php?id=10865}
} 
