Power law Stokes equations with threshold slip boundary conditions : numerical methods and implementation

dc.contributor.authorDjoko, J.K. (Jules Kamdem)
dc.contributor.authorKoko, Jonas
dc.contributor.authorKucera, Radek
dc.contributor.emailjules.djokokamdem@up.ac.zaen_ZA
dc.date.accessioned2018-12-03T08:04:07Z
dc.date.issued2019-03
dc.description.abstractFor the power law Stokes equations driven by nonlinear slip boundary conditions of friction type, we propose three iterative schemes based on augmented Lagrangian approach and interior point method to solve the finite element approximation associated to the continuous problem. We formulate the variational problem which in this case is a variational inequality and construct the weak solution of the continuous problem. Next, we formulate two alternating direction methods based on augmented Lagrangian formalism in order to separate the velocity from the symmetric part the velocity gradient and tangential part of the velocity. Thirdly, we present some salient points of a path-following variant of the interior point method associated to the finite element approximation of the problem. Some numerical experiments are performed to confirm the validity of the schemes and allow us to compare them.en_ZA
dc.description.departmentMathematics and Applied Mathematicsen_ZA
dc.description.embargo2020-03-30
dc.description.librarianhj2018en_ZA
dc.description.sponsorshipR. Kucera was financially supported by the project No. 17-01747S of the Czech Science Foundation and further by The Ministry of Education, Youth and Sports from the National Programme of Sustainability (NPS II) project “IT4Innovations excellence in science- LQ1602”.en_ZA
dc.description.urihttp://wileyonlinelibrary.com/journal/mmaen_ZA
dc.identifier.citationDjoko, J., Koko, J. & Kucera, R. 2019, 'Power law Stokes equations with threshold slip boundary conditions: numerical methods and implementation', Mathematical Methods in Applied Sciences, vol. 42, no. 5, pp. 1488-1511.en_ZA
dc.identifier.issn0170-4214 (print)
dc.identifier.issn1099-1476 (online)
dc.identifier.other10.1002/mma.5443
dc.identifier.urihttp://hdl.handle.net/2263/67427
dc.language.isoenen_ZA
dc.publisherWileyen_ZA
dc.rights© 2018 John Wiley and Sons, Ltd. This is the pre-peer reviewed version of the following article : Power law Stokes equations with threshold slip boundary conditions: numerical methods and implementation, Mathematical Methods in Applied Sciences, vol. 42, no. 5, pp. 1488-1511, 2019, doi : 10.1002/mma.5443. The definite version is available at : http://wileyonlinelibrary.com/journal/mma.en_ZA
dc.subjectNonlinear Stokesen_ZA
dc.subjectAugmented Lagrangianen_ZA
dc.subjectInterior points methoden_ZA
dc.subjectAlternating direction method of multiplieren_ZA
dc.subjectSimulationsen_ZA
dc.titlePower law Stokes equations with threshold slip boundary conditions : numerical methods and implementationen_ZA
dc.typePostprint Articleen_ZA

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