no. 5
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

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.

DOI : 10.1051/m2an:2004039
Classification : 65N35
Keywords: Stokes problem, spectral methods, axisymmetric geometries 
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     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},
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     year = {2004},
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     doi = {10.1051/m2an:2004039},
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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

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