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He, Yinnian; Mei, Liquan; Shang, Yueqiang; Cui, Juan

Newton iterative parallel finite element algorithm for the steady Navier-Stokes equations. (English) Zbl 1203.76003

J. Sci. Comput. 44, No. 1, 92-106 (2010).
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.

Cited in 49 Documents

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 algorithm

Software:

UMFPACK
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Full Text: DOI

References:

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