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

摘要

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 is contained in 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.