ON THE STABILITY OF THE RESIDUAL-FREE BUBBLES FOR THE NAVIER-STOKES EQUATIONS

This paper considers the Galerkin finite element method for the incompressibleNavier-Stokes equations in two dimensions, where the finite-dimensional spaces employedconsist of piecewise polynomials enriched with residual-free bubble (RFB) functions. Thestability features of the residual-free bubble functions for the linearized Navier-Stokes equa-tions are analyzed in this work. It is shown that the enrichment of the velocity space bybubble functions stabilizes the numerical method for any value of the viscosity parameterfor triangular elements and for values of the viscosity parameter in the vanishing limit casefor quadrilateral elements.