A study of Nonlinear Galerkin Finite Element for time-dependent incompressible Navier-Stokes equation

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 ${\text{bL}}^2$ norm, which is optimal in nature, for linear finite element approximation, in view of the error estimate available in literature, in ${\text{bH}}^1$ norm.