Reformed post-processing Galerkin method for the Navier-Stokes equations

In this article we compare the post-processing Galerkin (PPG) method with the reformed PPG method of integrating the two-dimensional Navier-Stokes equations in the case of non-smooth initial data u(o) is an element of H-0(1)(Omega)(2) with divu(o) = 0 and f, f(t) is an element of L-infinity(R+; L-2 (Omega)(2)). We give the global error estimates with H-1 and L-2-norm for these methods. Moreover, if the data nu and the lim(t ->infinity) f(t) satisfy the uniqueness condition, the global error estimates with H-1 and L-2-norm are uniform in time t. The difference between the PPG method and the reformed PPG method is that their error bounds are of the same forms on the interval [1, infinity) and the reformed PPG method has a better error bound than the PPG method on the interval [0, 1].