A three‐step Oseen‐linearized finite element method for incompressible flows with damping

Abstract

This paper introduces a three-step Oseen-linearized finite element method for the 2D/3D steady incompressible Navier-Stokes equations with nonlinear damping term. Within this method, we solve a nonlinear problem over a coarse grid followed by solving two Oseen-linearized problems over a fine grid, which possess the same stiffness matrices with only various right-hand sides. We theoretically analyze the stability of the present method, and derive optimal error estimates of the finite element solutions. We conduct a series of numerical experiments which support the theoretical analysis and test the effectiveness of the proposed method. We demonstrate numerically that there is a significant improvement in the accuracy of the approximate solutions over those for the standard two-level method.