Newton iterative parallel finite element algorithm for the steady Navier-Stokes equations. (English) Zbl 1203.76003
Summary: 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 \(\Omega \) and computing a linear problem on a fine grid in some subdomains \(\Omega j \subset \Omega \) with \(j=1,\cdots ,M\) 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 \(h\ll H\). Finally, some numerical tests are made to demonstrate the the effectiveness of this algorithm.
MSC:
76-04 | Software, source code, etc. for problems pertaining to fluid mechanics |
76M10 | Finite element methods applied to problems in fluid mechanics |
76D05 | Navier-Stokes equations for incompressible viscous fluids |
65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
65H10 | Numerical computation of solutions to systems of equations |
65N22 | Numerical solution of discretized equations for boundary value problems involving PDEs |
65Y05 | Parallel numerical computation |
Keywords:
Navier-Stokes equations; Newton iterative method; two-grid method; local and parallel algorithmSoftware:
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