A Wavelet-Galerkin Scheme for the Navier-Stokes equations
نویسندگان
چکیده
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. MSC 2000: 46E35, 65N30, 41A17, 76D05, 65F35 keywords: Galerkin scheme, wavelets, multiscale and multilevel methods, saddle-point problems, Navier-Stokes equation, Newton scheme, preconditioning
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