Geodesic
Spectral element discretization of the vorticity, velocity and pressure formulation of the Stokes problem
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 40 (2006) no. 5, pp. 897-921

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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.

DOI : 10.1051/m2an:2006038
Classification : 35Q30, 65N35
Keywords: Stokes problem, vorticity, velocity and pressure formulation, spectral element methods 
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     title = {Spectral element discretization of the vorticity, velocity and pressure formulation of the {Stokes} problem},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {897--921},
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Amoura, Karima; Bernardi, Christine; Chorfi, Nejmeddine. Spectral element discretization of the vorticity, velocity and pressure formulation of the Stokes problem. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 40 (2006) no. 5, pp. 897-921. doi: 10.1051/m2an:2006038

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