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

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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 subsequent approximations are generated on a succession of higher-dimensional spaces 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 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 .

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Authors and Affiliations

  1. Faculty of Science, Xi'an Jiaotong University, Xi'an, 710049, P. R. China

    Yinnian He

  2. Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong kong

    Kam-Moon Liu & Weiwei Sun

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  1. Yinnian He
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  2. Kam-Moon Liu
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Correspondence to Yinnian He.

Additional information

The work of this author was supported in part by the NSF of China 10371095, City University of Hong Kong Research Project 7001093 Hong Kong and the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CityU 1084/02P)

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He, Y., Liu, KM. & Sun, W. Multi-level spectral galerkin method for the navier-stokes problem I : spatial discretization. Numer. Math. 101, 501–522 (2005). https://doi.org/10.1007/s00211-005-0632-3

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  • DOI: https://doi.org/10.1007/s00211-005-0632-3

Mathematics Subject Classification (2000)