Volume 49, Number 3, May-June 2015
|Page(s)||621 - 639|
|Published online||03 April 2015|
Spectral discretization of the Navier–Stokes equations coupled with the heat equation
1 Faculty of Sciences of Tunis,
University of Tunis El Manar, 2060
Presently at Laboratoire Jacques-Louis Lions, Université Pierre et
Marie Curie, 4 place
Paris cedex 05,
2 Faculty of Sciences of Tunis, University of Tunis El Manar, 2060 Tunis, Tunisia.
3 Laboratoire Jacques-Louis Lions, C.N.R.S and Université Pierre et Marie Curie, Boîte courrier 187, 4 place Jussieu, 75252 Paris cedex 05, France.
4 IPEIT-University of Tunis, 2 street Jawaher Lel Nehru-1089, Monfleury, Tunisia.
Revised: 21 July 2014
We consider the spectral discretization of the Navier–Stokes equations coupled with the heat equation where the viscosity depends on the temperature, with boundary conditions which involve the velocity and the temperature. This problem admits a variational formulation with three independent unknowns, the velocity, the pressure and the temperature. We prove optimal error estimates and present some numerical experiments which confirm the validity of the discretization.
Mathematics Subject Classification: 35K05 / 36Q30 / 80M22
Key words: Navier–Stokes equations / heat equation / spectral methods
© EDP Sciences, SMAI 2015
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