We analyze a new formulation of the Stokes equations in three-dimensional axisymmetric geometries, relying on Fourier expansion with respect to the angular variable: the problem for each Fourier coefficient is two-dimensional and has six scalar unknowns, corresponding to the vector potential and the vorticity. A spectral discretization is built on this formulation, which leads to an exactly divergence-free discrete velocity. We prove optimal error estimates.
Mots clés : Stokes problem, spectral methods, axisymmetric geometries
@article{M2AN_2004__38_5_781_0,
author = {Abdellatif, Nehla and Bernardi, Christine},
title = {A new formulation of the {Stokes} problem in a cylinder, and its spectral discretization},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {781--810},
publisher = {EDP-Sciences},
volume = {38},
number = {5},
year = {2004},
doi = {10.1051/m2an:2004039},
mrnumber = {2104429},
zbl = {1079.76055},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an:2004039/}
}
TY - JOUR AU - Abdellatif, Nehla AU - Bernardi, Christine TI - A new formulation of the Stokes problem in a cylinder, and its spectral discretization JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2004 SP - 781 EP - 810 VL - 38 IS - 5 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2004039/ DO - 10.1051/m2an:2004039 LA - en ID - M2AN_2004__38_5_781_0 ER -
%0 Journal Article %A Abdellatif, Nehla %A Bernardi, Christine %T A new formulation of the Stokes problem in a cylinder, and its spectral discretization %J ESAIM: Modélisation mathématique et analyse numérique %D 2004 %P 781-810 %V 38 %N 5 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2004039/ %R 10.1051/m2an:2004039 %G en %F M2AN_2004__38_5_781_0
Abdellatif, Nehla; Bernardi, Christine. A new formulation of the Stokes problem in a cylinder, and its spectral discretization. ESAIM: Modélisation mathématique et analyse numérique, Tome 38 (2004) no. 5, pp. 781-810. doi : 10.1051/m2an:2004039. http://www.numdam.org/articles/10.1051/m2an:2004039/
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