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On a multilevel approach for the two dimensional Navier–Stokes equations with finite elements

✍ Scribed by C. Calgaro; A. Debussche; J. Laminie

Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
377 KB
Volume
27
Category
Article
ISSN
0271-2091

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✦ Synopsis

We study if the multilevel algorithm introduced in Debussche et al. (Theor. Comput. Fluid Dynam., 7, 279±315 (1995)) and Dubois et al. (J. Sci. Comp., 8, 167±194 (1993)) for the 2D Navier±Stokes equations with periodic boundary conditions and spectral discretization can be generalized to more general boundary conditions and to ®nite elements. We ®rst show that a direct generalization, as in Calgaro et al. (Appl. Numer. Math., 21, 1±40 (1997)), for the Burgers equation, would not be very ef®cient. We then propose a new approach where the domain of integration is decomposed in subdomains. This enables us to de®ne localized small-scale components and we show that, in this context, there is a good separation of scales. We conclude that all the ingredients necessary for the implementation of the multilevel algorithm are present.

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