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

Purpose - The purpose of this paper is to propose a new stabilized finite volume element method for the Navier-Stokes problem. Design/methodology/approach - This new method is based on the multiscale enrichment and uses the lowest equal order finite element pairs P-1/P-1. Findings - The stability and convergence of the optimal order in H-1-norm for velocity and L-2-norm for pressure are obtained. Originality/value - Using a dual problem for the Navier-Stokes problem, the convergence of the optimal order in L-2-norm for the velocity is obtained. Finally, numerical example confirms the theory analysis and validates the effectiveness of this new method.