Error of the two-step BDF for the incompressible Navier-Stokes problem

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Author(s) : Etienne Emmrich

The paper is published : M2AN 38 (2004) 5, pp. 757 - 764

MSC 2000

35Q30 Stokes and Navier-Stokes equations
65M12 Stability and convergence of numerical methods
76D05 Navier-Stokes equations

Abstract :
The incompressible Navier-Stokes problem is discretized in time by the two-step backward differentiation formula. Error estimates are proved under feasible assumptions on the regularity of the exact solution avoiding hardly fulfillable compatibility conditions. Whereas the time-weighted velocity error is of optimal second order, the time-weighted error in the pressure is of first order. Suboptimal estimates are shown for a linearisation. The results cover both the two- and three-dimensional case.

Keywords : Incompressible Navier-Stokes equation, time discretisation, backward differentiation formula, error estimate, parabolic smoothing