Comparative Study of Space Iteration Methods Based on Nonconforming Finite Element for Stationary Navier-Stokes Equations

Abstract

Steady Navier-Stokes equations are solved by three different space iteration methods based on the lowest order nonconforming finite element pairs $\mathscr{P}_1\mathscr{N} \mathscr{C}-\mathscr{P}_1,$ including simple, Oseen, and Newton iterative methods. The stability and convergence of these methods are studied, and their CPU time and numerical convergence rate are discussed. Numerical results are in good agreement with theoretical findings. In particular, numerical experiments show that for large viscosity, the Newton method converges faster than to others, whereas the Oseen method is more suitable for the equations with small viscosity.