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...
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| 格式: | Journal article |
| 語言: | English |
| 出版: |
2000
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| 總結: | 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. |
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