Spectral approximation of the periodic-nonperiodic Navier-Stokes equations |
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Authors: | Christine Bernardi Yvon Maday Brigitte Métivet |
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Affiliation: | (1) Analyse Numérique, Université P. et M. Curie, Tour 55-65, 5è étage, 4 place Jussieu, F-75252 Paris Cedex 05, France;(2) Analyse Numérique, Université P. et M. Curie, Tour 55-65, 5è étage, 4 place Jussieu, F-75252 Paris Cedex 05, France;(3) O.N.E.R.A., 29 avenue de la Division Leclerc, F-92320 Chatillon, France;(4) Université Paris XII, Paris, France;(5) Present address: E.D.F. DER/IMA, 1 avenue du Général de Gaulle, F-92141 Clamart Cedex, France |
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Abstract: | Summary In order to approximate the Navier-Stokes equations with periodic boundary conditions in two directions and a no-slip boundary condition in the third direction by spectral methods, we justify by theoretical arguments an appropriate choice of discrete spaces for the velocity and the pressure. The compatibility between these two spaces is checked via an infsup condition. We analyze a spectral and a collocation pseudo-spectral method for the Stokes problem and a collocation pseudo-spectral method for the Navier-Stokes equations. We derive error bounds of spectral type, i.e. which behave likeM– whereM depends on the number of degrees of freedom of the method and represents the regularity of the data. |
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Keywords: | AMS(MOS): 65N30: 65N35 CR:G1.8 |
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