caa a22 4500 467939314 CHVBK 20180406153007.0 cr unu---uuuuu 170328e20061101xx s 000 0 eng 10.1007/s10444-004-7640-1 doi (NATIONALLICENCE)springer-10.1007/s10444-004-7640-1 Multi-level spectral Galerkin method for the Navier-Stokes equations, II: time discretization [Elektronische Daten] [Yinnian He, Kam-Moon Liu] A fully discrete multi-level spectral Galerkin method in space-time for the two-dimensional nonstationary Navier-Stokes problem is considered. The method is a multi-scale method in which the fully nonlinear Navier-Stokes problem is only solved on the lowest-dimensional space $H_{m_{1}}$ with the largest time step Δt 1; subsequent approximations are generated on a succession of higher-dimensional spaces $H_{m_{j}}$ with small time step Δt j by solving a linearized Navier-Stokes problem about the solution on the previous level. Some error estimates are also presented for the J-level spectral Galerkin method. The scaling relations of the dimensional numbers and time mesh widths that lead to optimal accuracy of the approximate solution in H 1-norm and L 2-norm are investigated, i.e., m j∼m j−1 3/2 , Δt j∼Δt j−1 3/2 , j=2,. . .,J. We demonstrate theoretically that a fully discrete J-level spectral Galerkin method is significantly more efficient than the standard one-level spectral Galerkin method. Springer, 2006 Navier-Stokes problem nationallicence multi-level nationallicence spectral Galerkin method nationallicence error estimate nationallicence He Yinnian Faculty of Science (State Key Laboratory of Multiphase Flow in Power Engineering), Xi'an Jiaotong University, Xi'an 710049, P. R. China aut Liu Kam-Moon Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong aut Advances in Computational Mathematics Kluwer Academic Publishers 25/4(2006-11-01), 403-433 1019-7168 25:4<403 2006 25 10444 https://doi.org/10.1007/s10444-004-7640-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10444-004-7640-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- He Yinnian Faculty of Science (State Key Laboratory of Multiphase Flow in Power Engineering), Xi'an Jiaotong University, Xi'an 710049, P. R. China aut NATIONALLICENCE 700 1- Liu Kam-Moon Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong aut NATIONALLICENCE 773 0- Advances in Computational Mathematics Kluwer Academic Publishers 25/4(2006-11-01), 403-433 1019-7168 25:4<403 2006 25 10444 Metadata rights reserved Springer special CC-BY-NC licence nationallicence SWISSBIB 467140065 BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer