Iterative methods in penalty finite element discretizations for the Steady Navier–Stokes equations

Three penalty finite element methods are designed to solve numerically the steady Navier–Stokes equations, where the Stokes, Newton, and Oseen iteration methods are used, respectively. Moreover, the stability analysis and error estimate for these nine algorithms are provided. Finally, the numerical tests confirm the theoretical results of the presented algorithms. Meanwhile, the numerical investigations are provided to show that the proposed methods are efficient for solving the steady Navier–Stokes equations with the different viscosity. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 74‐94, 2014