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A new formulation of the Stokes problem in a cylinder, and its spectral discretization

Published online by Cambridge University Press:  15 October 2004

Nehla Abdellatif
Affiliation:
École Nationale des Sciences de l'Informatique, Campus Universitaire, 2010 Manouba, Tunisia.
Christine Bernardi
Affiliation:
Laboratoire Jacques-Louis Lions, CNRS & Université Pierre et Marie Curie, B.C. 187, 4 place Jussieu, 75252 Paris Cedex 05, France. bernardi@ann.jussieu.fr.
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Abstract

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.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2004

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References

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