Approximation of the global attractor for the incompressible Navier-Stokes equations
This paper considers the asymptotic behaviour of a practical numerical approximation of the Navier-Stokes equations in Ω, a bounded subdomain of ℝ2. The scheme consists of a conforming finite element spatial discretization, combined with an order-preserving linearly implicit implementation of the se...
Hauptverfasser: | , |
---|---|
Format: | Journal article |
Sprache: | English |
Veröffentlicht: |
2000
|
Zusammenfassung: | This paper considers the asymptotic behaviour of a practical numerical approximation of the Navier-Stokes equations in Ω, a bounded subdomain of ℝ2. The scheme consists of a conforming finite element spatial discretization, combined with an order-preserving linearly implicit implementation of the second-order BDF method. It is shown that the method possesses a compact global attractor, which is upper semicontinuous with respect to the attractor of the underlying system in H1 (Ω). The proofs employ the techniques of G-stability, discrete Sobolev estimates for the Stokes operator similar to those of Heywood and Rannacher, semigroups of linear operators and attractor convergence theory in the context of multistep methods. |
---|