Abstract
AbstractA two‐level method in space and time for the time‐dependent Navier‐Stokes equations is considered in this article. The approximate solution uM∈HM is decomposed into the large eddy component v∈Hm(m < M) and the small eddy component w∈H. We obtain the large eddy component v by solving a standard Galerkin equation in a coarse‐level subspace Hm with a time step length k, whereas the small eddy component w is derived by solving a linear equation in an orthogonal complement subspace H with a time step length pk, where p is a positive integer. The analysis shows that our two‐level scheme has long‐time stability and can reach the same accuracy as the standard Galerkin method in fine‐level subspace HM for an appropriate configuration of p and m. Moreover, some numerical examples are provided to complement our theoretical analysis. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013
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