Reformed post-processing Galerkin method for the Navier-Stokes equations
2007
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
$u_0 \epsilon\in H^1_0(\Omega)^2$ with div$u_0=0$ and $f,~f_t\in
L^\infty(R^+;L^2(\Omega)^2)$. We give the global error estimates
with $H^1$ and $L^2$-norm
for these methods.
Moreover, if the data $\nu$
and the $\lim_{t \rightarrow \infty}f(t)$ 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 $[0,1]$.
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