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backward differentiation formula

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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Error of the two-step BDF for the incompressible Navier-Stokes problem
Etienne Emmrich
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 38 / Issue 5 / September 2004

Published online by Cambridge University Press:

15 October 2004, pp. 757-764

Print publication:

September 2004
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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.