Spectral approximation of the periodic nonperiodic Navier-Stokes equations
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.
scientific article; zbMATH DE number 3934370
scientific article