Premium
Two‐level Newton iterative method for the 2D/3D steady Navier‐Stokes equations
Author(s) -
He Yinnian,
Zhang Yan,
Shang Yueqiang,
Xu Hui
Publication year - 2012
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20695
Subject(s) - mathematics , convergence (economics) , newton's method , uniqueness , grid , finite element method , iterative method , stability (learning theory) , navier–stokes equations , partial differential equation , stokes problem , mathematical analysis , mathematical optimization , nonlinear system , geometry , computer science , mechanics , physics , quantum mechanics , machine learning , compressibility , economics , thermodynamics , economic growth
A combination method of the Newton iteration and two‐level finite element algorithm is applied for solving numerically the steady Navier‐Stokes equations under the strong uniqueness condition. This algorithm is motivated by applying the m Newton iterations for solving the Navier‐Stokes problem on a coarse grid and computing the Stokes problem on a fine grid. Then, the uniform stability and convergence with respect to ν of the two‐level Newton iterative solution are analyzed for the large m and small H and h << H . Finally, some numerical tests are made to demonstrate the effectiveness of the method. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2012