Optimal orders of convergence for the Fourier-Galerkin method for two-dimensional Navier-Stokes equations in various energy norms and in Lp-norms of the velocity field are proved. Optimal orders of convergence for the Fourier-collocation method are also proved. Extensions of these results to three-dimensional Navier-Stokes equations in the original form and the rotational from are presented. Semigroup formulations and the variation of constants formula are the essential tools in the analysis.
All Science Journal Classification (ASJC) codes
- Numerical Analysis
- Computational Mathematics
- Applied Mathematics