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Finite-Element Approximation of the Nonstationary Navier–Stokes Problem. Part IV: Error Analysis for Second-Order Time Discretization

1990; Society for Industrial and Applied Mathematics; Volume: 27; Issue: 2 Linguagem: Inglês

10.1137/0727022

1095-7170

John G. Heywood, Rolf Rannacher,

Numerical methods in engineering

This paper provides an error analysis for the Crank–Nicolson method of time discretization applied to spatially discrete Galerkin approximations of the nonstationary Navier–Stokes equations. Second-order error estimates are proven locally in time under realistic assumptions about the regularity of the solution. For approximations of an exponentially stable solution, these local error estimates are extended uniformly in time as ${\text{t}} \to \infty $.