American Institute of Mathematical Sciences

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September  2007, 8(2): 369-387. doi: 10.3934/dcdsb.2007.8.369

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

Yinnian He 1, and  R. M.M. Mattheij 2,

1. 

Faculty of Science, Xi'an Jiaotong University, Xi'an 710049
2. 

Department of Mathematics and Computing Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, Netherlands

Received  September 2006 Revised  March 2007 Published  June 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 $[0,1]$.
Keywords: Galerkin method, Post-processing Galerkin method, Error estimate., Navier-Stokes equations.
Mathematics Subject Classification: Primary: 35Q30, 65M60, 65N30; Secondary: 76D0.
Citation: Yinnian He, R. M.M. Mattheij. Reformed post-processing Galerkin method for the Navier-Stokes equations. Discrete and Continuous Dynamical Systems - B, 2007, 8 (2) : 369-387. doi: 10.3934/dcdsb.2007.8.369
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