Newton Iterative Parallel Finite Element Algorithm for?the Steady Navier-Stokes Equations

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• 作者：Yinnian He ; Liquan Mei ; Yueqiang Shang and Juan Cui
• 关键词：Navier ; Stokes equations ; Newton iterative method ; Two ; grid method ; Local and parallel algorithm
• 刊名：Journal of Scientific Computing
• 出版年：2010
• 出版时间：July, 2010
• 年：2010
• 卷：44
• 期：1
• 页码：92-106
• 全文大小：678.6 KB

文摘

A combination method of the Newton iteration and parallel finite element algorithm is applied for solving the steady Navier-Stokes equations under the strong uniqueness condition. This algorithm is motivated by applying the Newton iterations of m times for a nonlinear problem on a coarse grid in domain Ω and computing a linear problem on a fine grid in some subdomains Ω _j ⊂Ω with j=1,…,M in a parallel environment. Then, the error estimation of the Newton iterative parallel finite element solution to the solution of the steady Navier-Stokes equations is analyzed for the large m and small H and h≪H. Finally, some numerical tests are made to demonstrate the the effectiveness of this algorithm.