A Stabilized Finite Element Method For Generalized Incompressible Flowproblems.

Abstract

odelled by the Oseen equation (or linearized Navier-Stokes equation) containing a
dominating zeroth order term. The method consists in subtracting a mesh dependent term from
the formulation without compromising consistency, which also allows the use of equal order
interpolation for both velocity and pressure. The design of this mesh dependent term, as well as
the stabilization parameter involved, are suggested by bubble condensation. Numerical stability
and optimal order error estimates are proven in the natural norms for velocity and pressure.
Moreover, an L2() error estimate for the velocity is proved, and in this estimate the difference
between dominating diffusion and dominating convection is explicited. Numerical experiments
confirming these theoretical results are presented.