Analysis of a new stabilized finite volume element method based on multiscale enrichment for the Navier-Stokes problem

The purpose of this paper is to propose a new stabilized finite volume element method for the Navier-Stokes problem.

This new method is based on the multiscale enrichment and uses the lowest equal order finite element pairs P₁/P₁.

The stability and convergence of the optimal order in H¹-norm for velocity and L²-norm for pressure are obtained.

Using a dual problem for the Navier-Stokes problem, the convergence of the optimal order in L²-norm for the velocity is obtained. Finally, numerical example confirms the theory analysis and validates the effectiveness of this new method.