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Spectral Galerkin approximations for the Navier-Stokes equations: Uniform in time error estimates. (English) Zbl 0788.76063

Summary: We derive uniform in time optimal \(H^ 1\) and \(L^ 2\) error estimates for the spectral Galerkin approximations for the nonstationary Navier- Stokes equations. This is done without explicitly assuming exponential stability for a class of solutions corresponding to decaying external force fields.

MSC:

76M25 Other numerical methods (fluid mechanics) (MSC2010)
76D05 Navier-Stokes equations for incompressible viscous fluids
65N15 Error bounds for boundary value problems involving PDEs
35Q30 Navier-Stokes equations
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