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Numerische Mathematik

, Volume 101, Issue 3, pp 501–522 | Cite as

Multi-level spectral galerkin method for the navier-stokes problem I : spatial discretization

  • Yinnian HeEmail author
  • Kam-Moon Liu
  • Weiwei Sun
Article

Abstract

A multi-level spectral Galerkin method for the two-dimensional non-stationary Navier-Stokes equations is presented. The method proposed here is a multiscale method in which the fully nonlinear Navier-Stokes equations are solved only on a low-dimensional space Open image in new window subsequent approximations are generated on a succession of higher-dimensional spaces Open image in new window j=2, . . . ,J, by solving a linearized Navier-Stokes problem around the solution on the previous level. Error estimates depending on the kinematic viscosity 0<ν<1 are also presented for the J-level spectral Galerkin method. The optimal accuracy is achieved when Open image in new window We demonstrate theoretically that the J-level spectral Galerkin method is much more efficient than the standard one-level spectral Galerkin method on the highest-dimensional space Open image in new window .

Mathematics Subject Classification (2000)

35L70 65N30 76D06 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Faculty of ScienceXi'an Jiaotong UniversityXi'anP. R. China
  2. 2.Department of MathematicsCity University of Hong KongKowloonHong kong

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