Spectral discretization of the Stokes problem with mixed boundary conditions

Karima Amoura (1) , Christine Bernardi (2) , Nejmeddine Chorfi (3) , Samira Saadi (1)

1 UBMA - Université Badji Mokhtar [Annaba]
2 LJLL - Laboratoire Jacques-Louis Lions
3 Département de mathématiques [Tunis]

The variational formulation of the Stokes problem with three independent unknowns, the vorticity, the velocity and the pressure, was born to handle non standard boundary conditions which involve the normal component of the velocity and the tangential components of the vorticity. We propose an extension of this formulation to the case of mixed boundary conditions in a three-dimensional domain. Next we consider a spectral discretization of this problem. A detailed numerical analysis leads to error estimates for the three unknowns and numerical experiments conrm the interest of the discretization.

Domaines: Analyse numérique [cs.NA]

Karima Amoura, Christine Bernardi, Nejmeddine Chorfi, Samira Saadi. Spectral discretization of the Stokes problem with mixed boundary conditions. The Journal of Bentham Studies, 2012, pp. 42-61 (20). ⟨10.2174/97816080525471120101⟩. ⟨hal-00518127⟩