Abstract
Any solution of the Navier–Stokes equations in a three-dimensional axisymmetric domain admits a Fourier expansion with respect to the angular variable, and it can be noted that each Fourier coefficient satisfies a variational problem on the meridian domain, all problems being coupled due to the nonlinear convection term. We propose a discretization of these equations which combines Fourier truncation and finite element methods applied to each two-dimensional system. We perform the a priori and a posteriori analysis of this discretization.
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Belhachmi, Z., Bernardi, C., Deparis, S. et al. An Efficient Discretization of the Navier–Stokes Equations in an Axisymmetric Domain. Part 1: The Discrete Problem and its Numerical Analysis. J Sci Comput 27, 97–110 (2006). https://doi.org/10.1007/s10915-005-9035-y
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DOI: https://doi.org/10.1007/s10915-005-9035-y