Spectral element discretization of the vorticity, velocity and pressure formulation of the Stokes problem

Amoura, Karima; Bernardi, Christine; Chorfi, Nejmeddine

ESAIM: Modélisation mathématique et analyse numérique, Tome 40 (2006) no. 5, pp. 897-921.

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.

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