中文摘要：

This paper considers Stokes and Newton iterations to solve stationary NavierStokes equations based on the finite element discretization. We obtain new sufficient conditions of stability and convergence for the two iterations. Specifically, when 0 < σ =(N||f||-1)ν2≤1/(2+1), the Stokes iteration is stable and convergent, where N is defined in the paper. When 0 < σ 511, the Newton iteration is stable and convergent. This work gives a more accurate admissible range of data for stability and convergence of the two schemes,which improves the previous results. A numerical test is given to verify the theory.

英文摘要：

This paper considers Stokes and Newton iterations to solve stationary Navier- Stokes equations based on the finite element discretization. We obtain new sufficient conditions of stability and convergence for the two iterations. Specifically, when 0 〈 σ =N｜｜f｜｜-1/v2≤1/√2＋1 , the Stokes iteration is stable and convergent, where N is defined in the paper. When 0 〈 σ ≤5/11, the Newton iteration is stable and convergent. This work gives a more accurate admissible range of data for stability and convergence of the two schemes, which improves the previous results. A numerical test is given to verify the theory.