Belhachmi, Zakaria
Bernardi, Christine
Deparis, Simone
Hecht, Frédéric
A truncated Fourier/finite element discretization of the Stokes equations in an axisymmetric domain
Mathematical Models and Methods in Applied Sciences (M3AS)
10.1142/S0218202506001133
16
2
233-263
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.
Stokes equations;
axisymmetric domain;
Fourier truncation;
finite elements;
2006
http://dx.doi.org/10.1142/S0218202506001133;