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<title lang=en>On a multilevel approach for the two-dimensional Navier-Stokes equations with finite elements.</title>
<creator>Laminie, Jacques</creator>
<creator>Calgaro, Caterina</creator>
<creator>Debussche, Arnaud</creator>
<contributor>Laboratoire de Mathématiques Informatique et Applications (LAMIA) ; Université des Antilles et de la Guyane (UAG)</contributor>
<contributor>Laboratoire Paul Painlevé - UMR 8524 (LPP) ; Université de Lille, Sciences et Technologies - Centre National de la Recherche Scientifique (CNRS)</contributor>
<contributor>SImulations and Modeling for PArticles and Fluids (SIMPAF) ; Laboratoire Paul Painlevé - UMR 8524 (LPP) ; Université de Lille, Sciences et Technologies - Centre National de la Recherche Scientifique (CNRS) - Université de Lille, Sciences et Technologies - Centre National de la Recherche Scientifique (CNRS) - Inria Lille - Nord Europe ; Institut National de Recherche en Informatique et en Automatique (Inria) - Institut National de Recherche en Informatique et en Automatique (Inria)</contributor>
<contributor>Institut de Recherche Mathématique de Rennes (IRMAR) ; Université de Rennes 1 (UR1) - AGROCAMPUS OUEST - École normale supérieure - Rennes (ENS Rennes) - Institut National de Recherche en Informatique et en Automatique (Inria) - Institut National des Sciences Appliquées (INSA) - Université de Rennes 2 (UR2) - Centre National de la Recherche Scientifique (CNRS)</contributor>
<description>International audience</description>
<source>ISSN: 0271-2091</source>
<source>EISSN: 1097-0363</source>
<source>International Journal for Numerical Methods in Fluids</source>
<publisher>Wiley</publisher>
<identifier>hal-00730709</identifier>
<identifier>https://hal.archives-ouvertes.fr/hal-00730709</identifier>
<source>https://hal.archives-ouvertes.fr/hal-00730709</source>
<source>International Journal for Numerical Methods in Fluids, Wiley, 1998, 27 (1-4), pp.241-258</source>
<language>en</language>
<subject>[MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA]</subject>
<type>info:eu-repo/semantics/article</type>
<type>Journal articles</type>
<description lang=en>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.</description>
<date>1998</date>
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