Title:
|
Convergence towards weak solutions of the Navier-Stokes equations for a finite element approximation with numerical subgrid scale modeling
|
Author:
|
Badia, Santiago; Gutiérrez Santacreu, Juan Vicente
|
Other authors:
|
Universitat Politècnica de Catalunya. Departament de Resistència de Materials i Estructures a l'Enginyeria; Universitat Politècnica de Catalunya. (MC)2 - Grup de Mecànica Computacional en Medis Continus |
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. |
Subject(s):
|
-Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits -Navier-Stokes equations -Equacions de Navier-Stokes |
Rights:
|
|
Document type:
|
Article - Draft Report |
Share:
|
|