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Convergence towards weak solutions of the Navier-Stokes equations for a finite element approximation with numerical subgrid scale modeling
dc.contributor.author | Badia, Santiago |
dc.contributor.author | Gutiérrez Santacreu, Juan Vicente |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Resistència de Materials i Estructures a l'Enginyeria |
dc.date.accessioned | 2012-11-14T17:48:02Z |
dc.date.available | 2012-11-14T17:48:02Z |
dc.date.created | 2012 |
dc.date.issued | 2012 |
dc.identifier.citation | Badia, S.; Gutiérrez, J. V. "Convergence towards weak solutions of the Navier-Stokes equations for a finite element approximation with numerical subgrid scale modeling". 2012. |
dc.identifier.uri | http://hdl.handle.net/2117/16920 |
dc.description.abstract | Residual-based stabilized nite element techniques for the Navier-Stokes equations lead to numerical discretizations that provide convection stabilization as well as pressure stability without the need to satisfy an inf-sup condition. They can be motivated by using a variational multiscale framework, based on the decomposition of the uid velocity into a resolvable nite element component plus a modeled subgrid scale component. The subgrid closure acts as a large eddy simulation turbulence model, leading to accurate under-resolved simulations. However, even though variational multiscale formulations are increasingly used in the applied nite element community, their numerical analysis has been restricted to a priori estimates and convergence to smooth solutions only, via a priori error estimates. In this work we prove that some versions of these methods (based on dynamic and orthogonal closures) also converge to weak (turbulent) solutions of the Navier-Stokes equations. These results are obtained by using compactness results in Bochner-Lebesgue spaces. Navier-Stokes equations; stability; convergence; stabilized nite element methods; subgrid scales; variational multiscale methods. |
dc.format.extent | 35 p. |
dc.language.iso | eng |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits |
dc.subject.lcsh | Navier-Stokes equations |
dc.title | Convergence towards weak solutions of the Navier-Stokes equations for a finite element approximation with numerical subgrid scale modeling |
dc.type | External research report |
dc.subject.lemac | Equacions de Navier-Stokes |
dc.contributor.group | Universitat Politècnica de Catalunya. (MC)2 - Grup de Mecànica Computacional en Medis Continus |
dc.rights.access | Open Access |
local.identifier.drac | 11052502 |
dc.description.version | Preprint |
dc.relation.projectid | info:eu-repo/grantAgreement/EC/FP7/258443/EU/Computational Methods for Fusion Technology/COMFUS |
local.citation.author | Badia, S.; Gutiérrez, J. V. |
local.citation.publicationName | Convergence towards weak solutions of the Navier-Stokes equations for a finite element approximation with numerical subgrid scale modeling |
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