On a two-level finite element method for the incompressible Navier-Stokes equations

We consider the Galerkin )nite element method for the incompressible Navier–Stokes equations in two dimensions, where the )nite-dimensional space(s) employed consist of piecewise polynomials enriched with residual-free bubble functions. To )nd the bubble part of the solution, a two-level )nite element method (TLFEM) is described and its application to the Navier–Stokes equation is displayed. Numerical solutions employing the TLFEM are presented for three benchmark problems. We compare the numerical solutions using the TLFEM with the numerical solutions using a stabilized method