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Interpolating Wavelets applied to the Navier‐Stokes equations
Author(s) -
Faustino Nelson
Publication year - 2006
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200610348
Subject(s) - wavelet , solver , ansatz , mathematics , convergence (economics) , context (archaeology) , nonlinear system , galerkin method , quadrature (astronomy) , multiresolution analysis , legendre wavelet , mathematical analysis , mathematical optimization , wavelet transform , computer science , discrete wavelet transform , physics , paleontology , quantum mechanics , artificial intelligence , optics , economics , economic growth , mathematical physics , biology
We propose a Wavelet‐Galerkin scheme for the stationary Navier‐Stokes equations based on the application of interpolating wavelets. To overcome the problems of nonlinearity, we apply the machinery of interpolating wavelets presented in [2] 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. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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