On the time discretization for the globally modified three dimensional Navier–Stokes equations

dc.contributor.authorDeugoue, Gabriel
dc.contributor.authorDjoko, J.K. (Jules Kamdem)
dc.contributor.emailjules.djokokamdem@up.ac.zaen_US
dc.date.accessioned2011-04-28T07:09:37Z
dc.date.available2011-04-28T07:09:37Z
dc.date.issued2011-02
dc.description.abstractIn this work, we analyze the discrete in time 3D system for the globally modified Navier–Stokes equations introduced by Caraballo (2006) [1]. More precisely, we consider the backward implicit Euler scheme, and prove the existence of a sequence of solutions of the resulting equations by implementing the Galerkin method combined with Brouwer’s fixed point approach. Moreover, with the aid of discrete Gronwall’s lemmas we prove that for the time step small enough, and the initial velocity in the domain of the Stokes operator, the solution is H2 uniformly stable in time, depends continuously on initial data, and is unique. Finally, we obtain the limiting behavior of the system as the parameter N is big enough. In this work, we analyze the discrete in time 3D system for the globally modified Navier–Stokes equations introduced by Caraballo (2006) [1]. More precisely, we consider the backward implicit Euler scheme, and prove the existence of a sequence of solutions of the resulting equations by implementing the Galerkin method combined with Brouwer’s fixed point approach. Moreover, with the aid of discrete Gronwall’s lemmas we prove that for the time step small enough, and the initial velocity in the domain of the Stokes operator, the solution is H2 uniformly stable in time, depends continuously on initial data, and is unique. Finally, we obtain the limiting behavior of the system as the parameter N is big enough.en
dc.identifier.citationDeugoue, G & Djoko, JK 2011, 'On the time discretization for the globally modified three dimensional Navier-Stokes equations', Journal of Computational and Applied Mathematics, vol. 235, no. 5, pp. 2015-2029. [www.elsevier.com/locate/cam]en
dc.identifier.issn0377-0427
dc.identifier.issn1879-1778
dc.identifier.issn10.1016/j.cam.2010.10.003
dc.identifier.urihttp://hdl.handle.net/2263/16370
dc.language.isoenen_US
dc.publisherElsevieren_US
dc.rights© 2010 Elsevier B.V. All rights reserved.en_US
dc.subject3D-Navier–Stokes equationsen
dc.subjectDiscrete Gronwall lemmasen
dc.subjectImplicit Euler schemeen
dc.subjectContinuous dependenceen
dc.subjectUniquenessen
dc.subjectAbsorbing seten
dc.subject.lcshNavier-Stokes equationsen
dc.titleOn the time discretization for the globally modified three dimensional Navier–Stokes equationsen
dc.typePostprint Articleen

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