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

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.

Automated summary

This paper introduces a three-step Oseen-linearized finite element method for the 2D/3D steady incompressible Navier-Stokes equations with nonlinear damping term. We theoretically analyze the stability of the method and derive optimal error estimates of the finite element solutions. Numerical experiments support the theoretical analysis and demonstrate the effectiveness of the proposed method.