A truncated Fourier/finite element discretization of the Stokes equations in an axisymmetric domain

We consider the Stokes problem in a three-dimensional axisymmetric domain and, by writing the Fourier expansion of its solution with respect to the angular variable, we observe that each Fourier coefficient satisfies a system of equations on the meridian domain. We propose a discretization of this problem which combines Fourier truncation and finite element methods applied to each of the two-dimensional systems. We give the detailed a priori and a posteriori analyses of the discretization and present some numerical experiments which are in good agreement with the analysis.


Published in:
Mathematical Models and Methods in Applied Sciences (M3AS), 16, 2, 233-263
Year:
2006
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 Record created 2007-12-13, last modified 2018-03-17

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