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axisymmetric geometries.

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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A new formulation of the Stokes problem in a cylinder, and its spectral discretization
Nehla Abdellatif, Christine Bernardi
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 38 / Issue 5 / September 2004

Published online by Cambridge University Press:

15 October 2004, pp. 781-810

Print publication:

September 2004
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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.