Mathematical Problems in Engineering
Volume 2005 (2005), Issue 3, Pages 341-363

A multilevel method of nonlinear Galerkin type for the Navier-Stokes equations

Said El Hajji and Khalid Ilias

Department of Mathematics and Informatics, Faculty of Sciences, University Mohammed V-Agdal, Rabat B.P. 1014, Morocco

Received 21 October 2004

Copyright © 2005 Said El Hajji and Khalid Ilias. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The basic idea of this new method resides in the fact that the major part of the relative information to the solution to calculate is contained in the small modes of a development of Fourier series; the raised modes of which the coefficients associated being small, being negligible to every instant, however, the effect of these modes on a long interval of time is not negligible. The nonlinear Galerkin method proposes economical treatment of these modes that permits, in spite of a simplified calculation, taking into account their interaction correctly with the other modes. After the introduction of this method, we elaborate an efficient strategy for its implementation.