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dc.creatorGuillén González, Francisco Manueles
dc.creatorGutiérrez Santacreu, Juan Vicentees
dc.date.accessioned2016-05-16T11:12:01Z
dc.date.available2016-05-16T11:12:01Z
dc.date.issued2008
dc.identifier.citationGuillén González, F.M. y Gutiérrez Santacreu, J.V. (2008). Conditional stability and convergence of a fully discrete scheme for three-dimensional Navier–Stokes equations with mass diffusion. SIAM Journal on Mathematical Analysis, 46 (5), 2276-2308.es
dc.identifier.issn0036-1410es
dc.identifier.issn1095-7154es
dc.identifier.urihttp://hdl.handle.net/11441/41266
dc.description.abstractWe construct a fully discrete numerical scheme for three-dimensional incompressible fluids with mass diffusion (in density-velocity-pressure formulation), also called the Kazhikhov–Smagulov model. We will prove conditional stability and convergence, by using at most C0-finite elements, although the density of the limit problem will have H2-regularity. The key idea of our argument is first to obtain pointwise estimates for the discrete density by imposing the constraint lim(h,k)→0 h/k = 0 on the time and space parameters (k, h). Afterwards, under the same constraint on the parameters, strong estimates for the discrete density in l ∞(H1) and for the discrete Laplacian of the density in l 2(L2) are obtained. From here, the compactness and convergence of the scheme can be concluded with similar arguments as we used in [Math. Comp., to appear], where a different scheme is studied for two-dimensional domains which is unconditionally stable and convergent. Moreover, we study the asymptotic behavior of the numerical scheme as the diffusion parameter λ goes to zero, obtaining convergence as (k, h, λ) → 0 towards a weak solution of the density-dependent Navier–Stokes system provided that the constraint lim(λ,h,k)→0 h/(λ2k) = 0 on (h, k, λ) is satisfied.es
dc.description.sponsorshipMinisterio de Educación y Cienciaes
dc.formatapplication/pdfes
dc.language.isoenges
dc.publisherSociety for Industrial and Applied Mathematicses
dc.relation.ispartofSIAM Journal on Mathematical Analysis, 46(5), 2276-2308es
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 Internacional*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/*
dc.subjectthree-dimensional Kazhikhov–Smagulov modelses
dc.subjectdensity-dependent Navier–Stokes equationses
dc.subjectfinite elementses
dc.subjectstabilityes
dc.subjectconvergencees
dc.titleConditional stability and convergence of a fully discrete scheme for three-dimensional Navier–Stokes equations with mass diffusiones
dc.typeinfo:eu-repo/semantics/articlees
dcterms.identifierhttps://ror.org/03yxnpp24
dc.type.versioninfo:eu-repo/semantics/publishedVersiones
dc.rights.accessrightsinfo:eu-repo/semantics/openAccesses
dc.contributor.affiliationUniversidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numéricoes
dc.relation.projectIDBFM2003–06446-C02-01es
dc.identifier.doihttp://dx.doi.org/10.1137/07067951Xes
idus.format.extent33 p.es
dc.journaltitleSIAM Journal on Mathematical Analysises
dc.publication.volumen46es
dc.publication.issue5es
dc.publication.initialPage2276es
dc.publication.endPage2308es
dc.identifier.idushttps://idus.us.es/xmlui/handle/11441/41266
dc.contributor.funderMinisterio de Educación y Ciencia (MEC). España

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