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Guermond, J.L. (author), Prudhomme, S. (author)The purpose of this paper is to show that the Fourier-based Nonlinear Galerkin Method (NLGM) constructs suitable weak solutions to the periodic Navier--Stokes equations in three dimensions. We re-interpret NLGM as a Large-Eddy Simulation technique (LES) and we rigorously deduce a relationship between the mesh size and the large-eddy scale.conference paper 2006