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On a multilevel approach for the two dimensional Navier–Stokes equations with finite elements
Author(s) -
Calgaro C.,
Debussche A.,
Laminie J.
Publication year - 1998
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/(sici)1097-0363(199801)27:1/4<241::aid-fld662>3.0.co;2-4
Subject(s) - discretization , mathematics , domain decomposition methods , generalization , domain (mathematical analysis) , navier–stokes equations , context (archaeology) , boundary (topology) , finite element method , boundary value problem , scale (ratio) , mathematical analysis , compressibility , physics , paleontology , quantum mechanics , biology , thermodynamics
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 finite elements. We first 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 efficient. We then propose a new approach where the domain of integration is decomposed in 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. © 1998 John Wiley & Sons, Ltd.