A stabilization technique for steady flow problems

Finite element methods with stabilization techniques for the steady Navier-Stokes equations are studied. To solve the steady Navier-Stokes equations, the Newton method is used. To compute the problem at each step of the nonlinear iteration, a stabilization technique is introduced. The mixed interpolation, which satisfies the inf-sup condition, with stabilized terms is also considered to investigate its computational efficiency. Numerical results show that stabilized terms improve convergences of the Newton method especially in the case of high Reynolds numbers as well as those of the linear solver at each step of the nonlinear iteration.