A STABILIZED FINITE ELEMENT METHOD FOR THE LINEARIZED NAVIER-STOKES EQUATION WITH DOMINATING REACTION

lized method Abstract. A new stabilized nite element method is introduced for the linearized version of the Navier-Stokes equation, containing a dominating zeroth order term. The method consists in subtracting a mesh dependent term from the formulation without compromising consistency. The design of this mesh dependent term, as well as the stabilization parameter involved, are suggested by bubble condensation. Stability is proven for any combination of velocity and pressure spaces, under the hypotheses of continuity for the pressure space. Optimal order error estimates are derived for the velocity and the pressure, using the standard norms for these unknowns. Numerical experiments conrming these theoretical results are presented. 1 Gabriel R. Barrenechea and Miguel A. Fernande