Spectral element discretization of the vorticity, velocity and pressure formulation of the Stokes problem
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 40 (2006) no. 5, p. 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.

DOI : https://doi.org/10.1051/m2an:2006038
Classification:  35Q30,  65N35
Keywords: Stokes problem; vorticity, velocity and pressure formulation; spectral element methods
@article{M2AN_2006__40_5_897_0,
author = {Amoura, Karima and Bernardi, Christine and Chorfi, Nejmeddine},
title = {Spectral element discretization of the vorticity, velocity and pressure formulation of the Stokes problem},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {40},
number = {5},
year = {2006},
pages = {897-921},
doi = {10.1051/m2an:2006038},
zbl = {1109.76044},
mrnumber = {2293251},
language = {en},
url = {http://www.numdam.org/item/M2AN_2006__40_5_897_0}
}

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 - Modélisation Mathématique et Analyse Numérique, Volume 40 (2006) no. 5, pp. 897-921. doi : 10.1051/m2an:2006038. http://www.numdam.org/item/M2AN_2006__40_5_897_0/

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