06-27
An inf--sup stable and residual--free bubble element for the Oseen equations
by Franca, Leopoldo P.; John, Volker; Matthies, Gunar; Tobiska, Lutz
Preprint series: 06-27, 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 equations, nonconforming finite elements
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