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Analysis of newton multilevel stabilized finite volume method for the three‐dimensional stationary Navier‐Stokes equations
Author(s) -
Zhao Xin,
Li Jian,
Su Jian,
Lei Gang
Publication year - 2013
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.21798
Subject(s) - finite volume method , mathematics , finite element method , discretization , nonlinear system , uniqueness , partial differential equation , rate of convergence , convergence (economics) , navier–stokes equations , newton's method , mathematical analysis , computer science , mechanics , physics , compressibility , thermodynamics , economics , economic growth , computer network , channel (broadcasting) , quantum mechanics
Abstract This article proposes and analyzes a multilevel stabilized finite volume method(FVM) for the three‐dimensional stationary Navier–Stokes equations approximated by the lowest equal‐order finite element pairs. The method combines the new stabilized FVM with the multilevel discretization under the assumption of the uniqueness condition. The multilevel stabilized FVM consists of solving the nonlinear problem on the coarsest mesh and then performs one Newton correction step on each subsequent mesh thus only solving one large linear systems. The error analysis shows that the multilevel‐stabilized FVM provides an approximate solution with the convergence rate of the same order as the usual stabilized finite element solution solving the stationary Navier–Stokes equations on a fine mesh for an appropriate choice of mesh widths: h j ∼ h j ‐1 2 , j = 1,…, J . Therefore, the multilevel stabilized FVM is more efficient than the standard one‐level‐stabilized FVM. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013