Numerical approximation of attractor for Navier–Stokes equations

I. N. Kostin

Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 24, Tome 200 (1992), pp. 91-97

Résumé

In the paper it is considered the problem of numerical approximation of the minimal global $B$-attractor $\mathfrak{M}$ for the semiflow generated by Navier–Stokes equations in a two-dimentional bounded domain $\Omega$. The suggested method is based on the formula $\mathfrak{M}=\lim\limits_{N\to\infty}G^N$, $G^N$ being a sequence of compact subsets of $L_2(\Omega)$, $G^N\supset\mathfrak{M}$. The procedure for construction of $G^N$ is finite and includes numerical resolution of Navier–Stokes equations by means of Galerkin method along with explicit finite-difference discretization in time.