A finite element variational multiscale method for incompressible flow

In this paper, we present a numerical scheme, prove stability, existence of solutions, uniqueness and convergence of the incompressible Navier–Stokes equations. It has the advantage of being defined from strictly algebraic considerations. A significant feature of the present method is that the structure of the stabilization term based on the multiscale enrichment and derived from the Navier–Stokes problem itself. Ample numerical experiments are carried out to confirm the theory and illustrate the effectiveness of the scheme on incompressible fluid.