Author(s) :
Etienne Emmrich
The paper is published :
M. Feistauer, R. Rannacher, K. Kozel
(eds.), Numerical Modelling in Continuum Mechanics, pp. 98 - 106, Matfyzpress Prag 2001. Proc. of the 4th Summer Conference Prague,
August 2000
MSC 2000
- 65M12 Stability and convergence of numerical methods
-
65M15 Error bounds
-
76D05 Navier-Stokes equations
Abstract :
An overview of some recent results for
the temporal discretization of the incompressible
Navier-Stokes problem by means of the two-step backward
differentiation formula is given.
The original nonlinear
approximation as well as a variant based upon a
linearization of the convective term
are considered.
After studying solvability and stability,
convergence of a piecewise polynomial approximate solution
towards a weak solution is shown.
Furthermore, smoothing error estimates
-under realistic assumptions on the problem's data-
are presented
for the velocity as well as the pressure.
Keywords :
Incompressible Navier-Stokes equation, time
discretization, backward differentiation formula, stability,
convergence, error estimate