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2006-27

An inf--sup stable and residual--free

by Franca, Leopoldo P., John, Volker, Matthies, Gunar, Tobiska, Lutz.


Series: 2006-27, Preprints

MSC:
65N12 Stability and convergence of numerical methods
65N30 Finite elements, ~Rayleigh-Ritz and Galerkin methods, finite methods
65N15 Error bounds

Abstract:
We investigate the residual--free bubble method (RFB) for the linearized
incompressible Navier--Stokes equations. Starting with a nonconforming
inf--sup stable element pair for approximating the velocity and pressure,
we enrich the velocity space by discretely divergence free bubble functions
to handle the influence of strong convection. An important feature of the
method is that the stabilization does not generate an additional coupling
between the mass equation and the momentum equation as it is the case for
the streamline upwind Petrov Galerkin (SUPG) method applied to
equal order interpolation. Furthermore, the discrete solution is piecewise
divergence
free, a property which is useful for the mass balance in transport equations
coupled with the incompressible Navier--Stokes equations.

Keywords:
Stabilized finite elements, Navier--Stokes e