This contribution deals with the numerical realization of the Stokes system involving the local Coulomb slip boundary conditions. The algebraic formulation arising from a finite element approximation leads to a non-smooth system of algebraic equations which is solved by the semi-smooth Newton method using the active/inactive set strategy. Results of a model example are presented.
REFERENCES
1.
D.
Arnold
, F.
Brezzi
, M.
Fortin
, A stable finite element for the Stokes equations
, Calcolo
, 21
(1984
), 337
–344
.2.
IT4Innovations Documentation
: “National Supercomputing Center, VŠB - Technical University of Ostrava, Salomon Cluster Documentation
”. At: https://docs.it4i.cz/salomon/introduction.3.
J.
Haslinger
, R.
Kučera
, V.
Šátek
, Stokes system with local Coulombs slip boundary conditions: Analysis of discretized models and implementation
, Computers and Mathematics with Applications
, (2018
), doi: .4.
M.
Hintermüller
and K.
Ito
and K.
Kunisch
, The primal-dual active set strategy as a semismooth Newton method
, SIAM J. Optim.
, 13
(2013
), 865
–888
.5.
J.
Koko
, Vectorized Matlab codes for the Stokes problem with P1-bubble/P1 finite element, At
: http://www.isima.fr/jkoko/Codes.html [online], (2012
).6.
R.
Kučera
, J.
Machalová
, H.
Netuka
, P.
Ženčák
, An interior point algorithm for the minimization arising from 3D contact problems with friction
, Optim. Method Softw.
, 28
, 6
(2013
), 1195
–1217
.
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