A fully discrete nonLinear Galerkin method for the 3D Navier-Stokes equations

J. L. Guermond*, Serge Prudhomme

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

The purpose of this paper is twofold: (i) We show that the Fourier-based Nonlinear Galerkin Method (NLGM) constructs suitable weak solutions to the periodic Navier-Stokes equations in three space dimensions provided the large scale/small scale cutoff is appropriately chosen, (ii) If smoothness is assumed, NLGM always outperforms the Galerkin method by a factor equal to 1 in the convergence order of the H1-norm for the velocity and the L 2-norm for the pressure. This is a purely linear superconvergence effect resulting from standard elliptic regularity and holds independently of the nature of the boundary conditions (whether periodicity or no-slip BC is enforced).

Original languageEnglish (US)
Pages (from-to)759-775
Number of pages17
JournalNumerical Methods for Partial Differential Equations
Volume24
Issue number3
DOIs
StatePublished - May 1 2008

Keywords

  • Navier-Stokes equations
  • Nonlinear Galerkin method
  • Suitable solutions
  • Turbulence

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

Cite this