A finite element variational multiscale method for incompressible flow

Abstract 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.