Some iterative finite element methods for steady Navier–Stokes equations with different viscosities

Xu, Haibo; He, Yinnian

doi:10.1016/j.jcp.2012.07.020

Cited by 50 publications

(28 citation statements)

References 27 publications

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“…As shown in [18], using the Ladyzhenskaya inequality and the Poincaré-Friedrichs inequality we can take N to be 1/2π for the domain Ω = (0, 1) × (0, 1), where N is a generic constant such that (1.5) holds. We also have by numerical computation that f −1 is approximately equal to 0.89108.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Under the assumption that the triangulations are quasi-uniform so that the inverse inequalities hold for the underlying finite elements, the error analysis was also developed in this paper. In [18], several two-level iterative methods were designed for solving the previous problem in two and three dimensional cases, by combining different methods in [11] in fine and coarse meshes technically for different value of Λ given in (1.6). Moreover, the error analysis was also established under the similar conditions in [11].…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, the error analysis was also established under the similar conditions in [11]. We refer the reader to [11,18] and the references cited there for details along this line.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Some Uzawa methods for steady incompressible Navier–Stokes equations discretized by mixed element methods

Chen

Huang

Sheng

2015

Journal of Computational and Applied Mathematics

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Some Uzawa methods for steady incompressible Navier–Stokes equations discretized by mixed element methods

Chen

Huang

Sheng

2015

Journal of Computational and Applied Mathematics

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“…Lots of works have investigated the stationary Navier-Stokes problem [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] . There are also numerous works devoted to the development of efficient schemes for the nonstationary Navier-Stokes problem [16][17][18][19][20][21][22][23][24] .…”

Section: Introductionmentioning

confidence: 99%

“…Besides, the Oseen scheme is unconditionally stable and convergent under 0 < σ < 1 [9,25] . Recently, the stability and convergence condition of the Newton iteration was improved [10,15] , and the improved condition is 0 < σ 1 3 . In the present paper, using a new proof technique, we obtain the more accurate conditions of stability and convergence of the Stokes and Newton schemes, and the new results are 0 < σ 1 √ 2+1 and 0 < σ 5 11 , respectively.…”

Section: Introductionmentioning

confidence: 99%

New conditions of stability and convergence of Stokes and Newton iterations for Navier-Stokes equations

Zhang

Xiang

et al. 2015

Appl. Math. Mech.-Engl. Ed.

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This paper considers Stokes and Newton iterations to solve stationary NavierStokes equations based on the finite element discretization. We obtain new sufficient conditions of stability and convergence for the two iterations. Specifically, when 0 < σ = N||f || −1 ν 2 1 √ 2+1 , the Stokes iteration is stable and convergent, where N is defined in the paper. When 0 < σ 5 11 , the Newton iteration is stable and convergent. This work gives a more accurate admissible range of data for stability and convergence of the two schemes, which improves the previous results. A numerical test is given to verify the theory.

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Two‐level consistent splitting methods based on three corrections for the time‐dependent Navier–Stokes equations

Liu

Hou

Wang

et al. 2015

Numerical Methods in Fluids

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Summary Three kinds of two‐level consistent splitting algorithms for the time‐dependent Navier–Stokes equations are discussed. The basic technique of two‐level type methods for solving the nonlinear problem is first to solve a nonlinear problem in a coarse‐level subspace, then to solve a linear equation in a fine‐level subspace. Hence, the two‐level methods can save a lot of work compared with the one‐level methods. The approaches to linearization are considered based on Stokes, Newton, and Oseen corrections. The stability and convergence demonstrate that the two‐level methods can acquire the optimal accuracy with the proper choice of the coarse and fine mesh scales. Numerical examples show that Stokes correction is the simplest, Newton correction has the best accuracy, while Oseen correction is preferable for the large Reynolds number problems and the long‐time simulations among the three methods. Copyright © 2015 John Wiley & Sons, Ltd.

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Some iterative finite element methods for steady Navier–Stokes equations with different viscosities

Cited by 50 publications

References 27 publications

Some Uzawa methods for steady incompressible Navier–Stokes equations discretized by mixed element methods

Some Uzawa methods for steady incompressible Navier–Stokes equations discretized by mixed element methods

New conditions of stability and convergence of Stokes and Newton iterations for Navier-Stokes equations

Two‐level consistent splitting methods based on three corrections for the time‐dependent Navier–Stokes equations

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