An inf-sup Stable and Residual-Free Bubble Element for the Oseen Equations

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.