A new formulation of the Stokes problem in a cylinder, and its spectral discretization
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 38 (2004) no. 5, p. 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 : https://doi.org/10.1051/m2an:2004039
Classification:  65N35
Keywords: 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: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {38},
     number = {5},
     year = {2004},
     pages = {781-810},
     doi = {10.1051/m2an:2004039},
     zbl = {1079.76055},
     mrnumber = {2104429},
     language = {en},
     url = {http://www.numdam.org/item/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: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 38 (2004) no. 5, pp. 781-810. doi : 10.1051/m2an:2004039. http://www.numdam.org/item/M2AN_2004__38_5_781_0/

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