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Journal Articles International Journal for Numerical Methods in Fluids Year : 1998

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

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Abstract

We study if the multilevel algorithm introduced by Debussche, T. Dubois and R. Temam [Theoret. Comput. Fluid Dynam. 7 (1995), no. 4, 279-315; Zbl 838.76060] and Dubois, F. Jauberteau and Temam [J. Sci. Comput. 8 (1993), no. 2, 167-194; MR1242960 (94f:65098)] for the 2D Navier-Stokes equations with periodic boundary conditions and spectral discretization can be generalized to more general boundary conditions and to finite elements. We first show that a direct generalization, as in [C. Calgaro, J. Laminie and R. Temam, Appl. Numer. Math. 23 (1997), no. 4, 403-442; MR1453424 (98d:76124)], for the Burgers equation, would not be very efficient. We then propose a new approach where the domain of integration is decomposed into subdomains. This enables us to define 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.

Dates and versions

hal-00730709 , version 1 (11-09-2012)

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Jacques Laminie, Caterina Calgaro, Arnaud Debussche. On a multilevel approach for the two-dimensional Navier-Stokes equations with finite elements. International Journal for Numerical Methods in Fluids, 1998, 27 (1-4), pp.241-258. ⟨10.1002/(SICI)1097-0363(199801)27:1/4<241::AID-FLD662>3.0.CO;2-4⟩. ⟨hal-00730709⟩
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