Spectral Element Discretization of the Circular Driven Cavity. Part IV: The Navier-Stokes Equations |
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| Authors: | Zakaria Belhachmi Christine Bernardi Andreas Karageorghis |
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| Affiliation: | (1) Laboratoire de Mathématiques (L.M.A.M.), U.M.R. 7122, Université de Metz, Ile de Saulcy, 57045 Metz Cedex 01, France;(2) Laboratoire Jacques-Louis Lions, C.N.R.S. & Université Pierre et Marie Curie, 4, place Jussieu, B.C. 187, 75252 Paris Cedex 05, France;(3) Dept. of Mathematics and Statistics, University of Cyprus, 20537, 1678 Nicosia, Cyprus |
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| Abstract: | This paper deals with the spectral element discretizationof the Navier-Stokes equations in a disk with discontinuousboundary data, which is known as the driven cavity problem.The numerical treatment does not involve any regularization of these data. Relying on a variationalformulation in the primitive variables of velocity and pressure, we describe a discretization of these equations andderive error estimates in appropriate weighted Sobolev spaces.We propose an algorithm to solve the nonlinear discrete system and present numerical experiments to verify itsefficiency. |
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| Keywords: | 65N35 35Q30 |
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