Error of the two-step BDF for the incompressible Navier-Stokes problem
Institut für Mathematik,
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Germany.
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.
Mathematics Subject Classification: 35Q30 / 65M12 / 76D05
Key words: Incompressible Navier-Stokes equation / time discretisation / backward differentiation formula / error estimate / parabolic smoothing.
© EDP Sciences, SMAI, 2004