S. Badia, J. Gutiérrez-Santacreu
Residual-based stabilized finite element (FE) 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 (VMS) framework, based on the decomposition of the fluid velocity into a resolvable FE component plus a modelled subgrid-scale component. The subgrid closure acts as a large eddy simulation turbulence model, leading to accurate under-resolved simulations. However, even though VMS formulations are increasingly used in the applied FE 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.
Published on 01/01/2014
DOI: 10.1093/imanum/drt023Licence: CC BY-NC-SA license
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