Abstract
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.
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