Abstract
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 ? and computing a linear problem on a fine grid in some subdomains ? j ?? 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.
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