%0 Journal Article
%T Stability of a colocated finite volume scheme for the incompressible Navier-Stokes equations
%A Sebastien Zimmermann
%J Mathematics
%D 2007
%I arXiv
%X We introduce a finite volume scheme for the two-dimensional incompressible Navier-Stokes equations. We use a triangular mesh. The unknowns for the velocity and pressure are both piecewise constant (colocated scheme). We use a projection (fractional-step) method to deal with the incompressibility constraint. We prove that the differential operators in the Navier-Stokes equations and their discrete counterparts share similar properties. In particular, we state an inf-sup (Babuska-Brezzi) condition. We infer from it the stability of the scheme.
%U http://arxiv.org/abs/0704.0772v1