  In this article, we discuss a couple of nonlinear Galerkin methods (NLGM) in
finite element set up for time dependent incompressible Navier-Sotkes
equations. We show the crucial role played by the non-linear term in
determining the rate of convergence of the methods. We have obtained improved
error estimate in $\bL^2$ norm, which is optimal in nature, for linear finite
element approximation, in view of the error estimate available in literature,
in $\bH^1$ norm.
