An Improved Arrow-Hurwicz Method for the Steady-State Navier-Stokes Equations

Abstract

This paper presents a novel Arrow-Hurwicz type method for approximating the steady-state Navier Stokes equations using the finite element method. The novel method is inspired from artificial compressibility regularization of unsteady incompressible flows and allows one to circumvent solving saddle-point equations. We derive uniform boundedness and convergence to the exact solution whenever the small data condition for uniqueness of the solution is satisfied. A two-grid version of the scheme is also discussed. Numerical schemes show that the novel scheme significantly accelerates the convergence, without any additional computational cost or decreased accuracy.