A Wavelet-Galerkin Scheme for the Navier-Stokes equations

We propose a Wavelet-Galerkin scheme for the stationary NavierStokes equations based on the application of interpolating wavelets. To overcome the problems of nonlinearity, we apply the machinery of interpolating wavelets presented in [10] and [13] in order to obtain problem-adapted quadrature rules. Finally, we apply Newton’s method to approximate the solution in the given ansatz space, using as inner solver a steepest descendent scheme. To obtain approximations of a higher accuracy, we apply our scheme in a multi-scale context. Special emphasize will be given for the convergence of the scheme and wavelet preconditioning.