A new formulation of the Stokes problem in a cylinder, and its spectral discretization
École Nationale des Sciences de
l'Informatique, Campus Universitaire, 2010 Manouba,
2 Laboratoire Jacques-Louis Lions, CNRS & Université Pierre et Marie Curie, B.C. 187, 4 place Jussieu, 75252 Paris Cedex 05, France. firstname.lastname@example.org.
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