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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| Format: | Journal article |
| Language: | English |
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2000
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| _version_ | 1826285921766473728 |
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| author | Hill, A Suli, E |
| author_facet | Hill, A Suli, E |
| author_sort | Hill, A |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T01:36:05Z |
| format | Journal article |
| id | oxford-uuid:953aaed1-1db9-420b-8959-c4b4fe6bd5e9 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T01:36:05Z |
| publishDate | 2000 |
| record_format | dspace |
| spelling | oxford-uuid:953aaed1-1db9-420b-8959-c4b4fe6bd5e92022-03-26T23:44:48ZApproximation of the global attractor for the incompressible Navier-Stokes equationsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:953aaed1-1db9-420b-8959-c4b4fe6bd5e9EnglishSymplectic Elements at Oxford2000Hill, ASuli, EThis 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. |
| spellingShingle | Hill, A Suli, E Approximation of the global attractor for the incompressible Navier-Stokes equations |
| title | Approximation of the global attractor for the incompressible Navier-Stokes equations |
| title_full | Approximation of the global attractor for the incompressible Navier-Stokes equations |
| title_fullStr | Approximation of the global attractor for the incompressible Navier-Stokes equations |
| title_full_unstemmed | Approximation of the global attractor for the incompressible Navier-Stokes equations |
| title_short | Approximation of the global attractor for the incompressible Navier-Stokes equations |
| title_sort | approximation of the global attractor for the incompressible navier stokes equations |
| work_keys_str_mv | AT hilla approximationoftheglobalattractorfortheincompressiblenavierstokesequations AT sulie approximationoftheglobalattractorfortheincompressiblenavierstokesequations |