| Issue |
ESAIM: M2AN
Volume 38, Number 5, September-October 2004
|
|
|---|---|---|
| Page(s) | 781 - 810 | |
| DOI | https://doi.org/10.1051/m2an:2004039 | |
| Published online | 15 October 2004 | |
A new formulation of the Stokes problem in a cylinder, and its spectral discretization
1
École Nationale des Sciences de
l'Informatique, Campus Universitaire, 2010 Manouba,
Tunisia.
2
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.
Received:
16
May
2003
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.
Mathematics Subject Classification: 65N35
Key words: Stokes problem / spectral methods / axisymmetric geometries.
© EDP Sciences, SMAI, 2004
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