Reformed post-processing Galerkin method for the Navier-Stokes equation (Q2467054)

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 \(u_0\in H^1_0(\Omega)^2\) with \(\text{div} u_0= 0\) and \(f, f_t\in L^\infty(\mathbb{R}^+;L^2(\Omega)^2)\). We give the global error estimates with \(H^1\) and \(L^2\)-norm for these methods. Moreover, if the data \(v\) and the \(\lim_{t\to\infty}f(t)\) 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 \([1,\infty)\) and the reformed PPG method has a better error bound than the PPG method on the interval \([0, 1]\).