dc.creator | Guillén González, Francisco Manuel | es |
dc.creator | Gutiérrez Santacreu, Juan Vicente | es |
dc.date.accessioned | 2016-05-16T11:12:01Z | |
dc.date.available | 2016-05-16T11:12:01Z | |
dc.date.issued | 2008 | |
dc.identifier.citation | Guillén 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.issn | 0036-1410 | es |
dc.identifier.issn | 1095-7154 | es |
dc.identifier.uri | http://hdl.handle.net/11441/41266 | |
dc.description.abstract | We 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.sponsorship | Ministerio de Educación y Ciencia | es |
dc.format | application/pdf | es |
dc.language.iso | eng | es |
dc.publisher | Society for Industrial and Applied Mathematics | es |
dc.relation.ispartof | SIAM Journal on Mathematical Analysis, 46(5), 2276-2308 | es |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 Internacional | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
dc.subject | three-dimensional Kazhikhov–Smagulov models | es |
dc.subject | density-dependent Navier–Stokes equations | es |
dc.subject | finite elements | es |
dc.subject | stability | es |
dc.subject | convergence | es |
dc.title | Conditional stability and convergence of a fully discrete scheme for three-dimensional Navier–Stokes equations with mass diffusion | es |
dc.type | info:eu-repo/semantics/article | es |
dcterms.identifier | https://ror.org/03yxnpp24 | |
dc.type.version | info:eu-repo/semantics/publishedVersion | es |
dc.rights.accessrights | info:eu-repo/semantics/openAccess | es |
dc.contributor.affiliation | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico | es |
dc.relation.projectID | BFM2003–06446-C02-01 | es |
dc.identifier.doi | http://dx.doi.org/10.1137/07067951X | es |
idus.format.extent | 33 p. | es |
dc.journaltitle | SIAM Journal on Mathematical Analysis | es |
dc.publication.volumen | 46 | es |
dc.publication.issue | 5 | es |
dc.publication.initialPage | 2276 | es |
dc.publication.endPage | 2308 | es |
dc.identifier.idus | https://idus.us.es/xmlui/handle/11441/41266 | |
dc.contributor.funder | Ministerio de Educación y Ciencia (MEC). España | |