Multi-level spectral Galerkin method for the Navier-Stokes equations, II : Time discretization

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journal

23 Scopus Citations
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Detail(s)

Original languageEnglish
Pages (from-to)403-433
Journal / PublicationAdvances in Computational Mathematics
Volume25
Issue number4
Publication statusPublished - Nov 2006

Abstract

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 Hm1 with the largest time step Δt 1; subsequent approximations are generated on a succession of higher-dimensional spaces Hmj 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.

Research Area(s)

  • Error estimate, Multi-level, Navier-Stokes problem, Spectral Galerkin method