Abstract
The two-dimensional Navier–Stokes equations, when subject to non-standard boundary conditions which involve the normal component of the velocity and the vorticity, admit a variational formulation with three independent unknowns, the vorticity, velocity and pressure. We propose a discretization of this problem by spectral element methods. A detailed numerical analysis leads to optimal error estimates for the three unknowns and numerical experiments confirm the interest of the discretization.
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Amoura, K., Azaïez, M., Bernardi, C. et al. Spectral element discretization of the vorticity, velocity and pressure formulation of the Navier–Stokes problem. Calcolo 44, 165–188 (2007). https://doi.org/10.1007/s10092-007-0135-y
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DOI: https://doi.org/10.1007/s10092-007-0135-y