Spectral approximation of the periodic nonperiodic Navier-Stokes equations. (English) Zbl 0583.65085

In order to approximate the Navier-Stokes equations with periodic boundary conditions in two directions and a no-slip boundary condition in the third direction by spectral methods, we justify by theoretical arguments an appropriate choice of discrete spaces for the velocity and the pressure. The compatibility between these two spaces is checked via an inf-sup condition. We analyze a spectral and a collocation pseudo- spectral method for the Stokes problem and a collocation pseudo-spectral method for the Navier-Stokes equations. We derive error bounds of spectral type, i.e. which behave like \(M^{-\sigma}\), where M depends on the number of degrees of freedom of the method and \(\sigma\) represents the regularity of the data.


65Z05 Applications to the sciences
76D05 Navier-Stokes equations for incompressible viscous fluids
35Q30 Navier-Stokes equations
65N15 Error bounds for boundary value problems involving PDEs
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
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