A new defect‐correction method for the stationary Navier–Stokes equations based on local Gauss integration

Huang, Pengzhan; He, Yinnian; Feng, Xinlong

doi:10.1002/mma.1618

Cited by 7 publications

(8 citation statements)

References 23 publications

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“…Theorem Assume that

boldf \in X^{'}

, then the defect iterative scheme of the above new defect‐correction method is unconditionally stable and

false({boldu}_{h}^{m}, p_{h}^{m} false)

defined by the scheme satisfies

\begin{matrix} false‖ \nabla u_{h}^{m} ‖_{0} & \leq ν^{- 1} false‖ boldf ‖_{- 1}, \\ false‖ p_{h}^{m} ‖_{0} & \leq β^{- 1} false(N ν^{- 2} false‖ boldf ‖_{- 1}^{2} + false‖ boldf ‖_{- 1} false) . \end{matrix}

The proof for this theorem is similar to the article …”

Section: Stability and Error Analysismentioning

confidence: 86%

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A new defect‐correction method for the stationary Navier‐Stokes equations based on pressure projection

Wen

2017

Math Methods in App Sciences

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A new defect-correction method based on the pressure projection for the stationary Navier-Stokes equations is proposed in this paper. A local stabilized technique based on the pressure projection is used in both defect step and correction step. The stability and convergence of this new method is analyzed detailedly. Finally, numerical examples confirm our theory analysis and validate high efficiency and good stability of this new method.

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“…Theorem Assume that

boldf \in X^{'}

, then the defect iterative scheme of the above new defect‐correction method is unconditionally stable and

false({boldu}_{h}^{m}, p_{h}^{m} false)

defined by the scheme satisfies

\begin{matrix} false‖ \nabla u_{h}^{m} ‖_{0} & \leq ν^{- 1} false‖ boldf ‖_{- 1}, \\ false‖ p_{h}^{m} ‖_{0} & \leq β^{- 1} false(N ν^{- 2} false‖ boldf ‖_{- 1}^{2} + false‖ boldf ‖_{- 1} false) . \end{matrix}

The proof for this theorem is similar to the article …”

Section: Stability and Error Analysismentioning

confidence: 86%

“…Wang also gave a new defect‐correction method for the Navier‐stokes equations with high Reynolds number. Moreover, Huang et al proposed a new defect correction based on local Gauss integration and a new two‐level defect‐correction Oseen iterative method for the Navier‐stokes equations,respectively.…”

Section: Introductionmentioning

confidence: 99%

A new defect‐correction method for the stationary Navier‐Stokes equations based on pressure projection

Wen

2017

Math Methods in App Sciences

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“…Zheng et al , provedthe equivalence between classical variational multiscale method and the variational multiscale method based on two local Gauss integrations. Huang et al , presented a new defect‐correction method for the stationary Navier‐Stokes equations based on two local Gauss integration.…”

Section: Introductionmentioning

confidence: 99%

A new two grid variational multiscale method for steady‐state natural convection problem

Kong

Yang

2016

Math Methods in App Sciences

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A two-grid variational multiscale method based on two local Gauss integrations for solving the stationary natural convection problem is presented in this article. A significant feature of the method is that we solve the natural convection problem on a coarse mesh using finite element variational multiscale method based on two local Gauss integrations firstly, and then find a fine grid solution by solving a linearized problem on a fine grid. In the computation, we introduce two local Gauss integrations as a stabilizing term to replace the projection operator without adding other variables. The stability estimates and convergence analysis of the new method are derived. Ample numerical experiments are performed to validate the theoretical predictions and demonstrate the efficiency of the new method.

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“…In [7] the method is extended to include adaptivity, multilevel refinement, domain decomposition and regredding. The LDC method is combined with finite volume discretizations in [5] and finite elements discretizations in [1,2].…”

Section: Introductionmentioning

confidence: 99%

Analysis of a Fourth Order Scheme and Application of Local Defect Correction Method

Abbas¹

2014

Journal of applied mathematics & informatics

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This paper provides a new application similar to the Local Defect Correction (LDC) technique to solve Poisson problem −u ′′ (x) = f (x) with Dirichlet boundary conditions. The exact solution is supposed to have high activity in some region of the domain. LDC is combined with a fourth order compact scheme which is recently developed in Abbas (Num. Meth. Partial differential equations, 2013). Numerical tests illustrate the interest of this application.

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A new defect‐correction method for the stationary Navier–Stokes equations based on local Gauss integration

Cited by 7 publications

References 23 publications

A new defect‐correction method for the stationary Navier‐Stokes equations based on pressure projection

A new defect‐correction method for the stationary Navier‐Stokes equations based on pressure projection

A new two grid variational multiscale method for steady‐state natural convection problem

Analysis of a Fourth Order Scheme and Application of Local Defect Correction Method

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