Spectral element discretization of the vorticity, velocity and pressure formulation of the Stokes problem
Université Badji-Mokhtar, Faculté des Sciences, Département de Mathématiques, B.P. 12, 23000 Annaba, Algeria.
2 Laboratoire Jacques-Louis Lions, C.N.R.S. et Université Pierre et Marie Curie, B.C. 187, 4 place Jussieu, 75252 Paris Cedex 05, France.
3 Département de Mathématiques, Faculté des Sciences de Tunis, Campus Universitaire, 1060 Tunis, Tunisia.
Revised: 13 June 2006
We consider the Stokes problem provided with non standard boundary conditions which involve the normal component of the velocity and the tangential components of the vorticity. We write a variational formulation of this problem with three independent unknowns: the vorticity, the velocity and the pressure. Next we propose a discretization by spectral element methods which relies on this formulation. A detailed numerical analysis leads to optimal error estimates for the three unknowns and numerical experiments confirm the interest of the discretization.
Mathematics Subject Classification: 35Q30 / 65N35
Key words: Stokes problem; vorticity / velocity and pressure formulation; spectral element methods.
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