Stabilized finite-element method for the stationary Navier-Stokes equations

Yinnian He; Aiwen Wang; Liquan Mei

doi:10.1007/s10665-004-3718-5

Stabilized finite-element method for the stationary Navier-Stokes equations

Yinnian He
, Aiwen Wang
, Liquan Mei

School of Mathematics and Statistics

Xi'an Jiaotong University
Beijing Institute of Machinery

Research output: Contribution to journal › Article › peer-review

69 Scopus citations

Abstract

A stabilized finite-element method for the two-dimensional stationary incompressible Navier-Stokes equations is investigated in this work. A macroelement condition is introduced for constructing the local stabilized formulation of the stationary Navier-Stokes equations. By satisfying this condition, the stability of the Q₁ - P₀ quadrilateral element and the P₁ - P₀ triangular element are established. Moreover, the well-posedness and the optimal error estimate of the stabilized finite-element method for the stationary Navier-Stokes equations are obtained. Finally, some numerical tests to confirm the theoretical results of the stabilized finite-element method are provided.

Original language	English
Pages (from-to)	367-380
Number of pages	14
Journal	Journal of Engineering Mathematics
Volume	51
Issue number	4
DOIs	https://doi.org/10.1007/s10665-004-3718-5
State	Published - Apr 2005

Keywords

Error estimation
Navier-Stokes equations
Stabilized finite element

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10.1007/s10665-004-3718-5

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title = "Stabilized finite-element method for the stationary Navier-Stokes equations",

abstract = "A stabilized finite-element method for the two-dimensional stationary incompressible Navier-Stokes equations is investigated in this work. A macroelement condition is introduced for constructing the local stabilized formulation of the stationary Navier-Stokes equations. By satisfying this condition, the stability of the Q1 - P0 quadrilateral element and the P1 - P0 triangular element are established. Moreover, the well-posedness and the optimal error estimate of the stabilized finite-element method for the stationary Navier-Stokes equations are obtained. Finally, some numerical tests to confirm the theoretical results of the stabilized finite-element method are provided.",

keywords = "Error estimation, Navier-Stokes equations, Stabilized finite element",

author = "Yinnian He and Aiwen Wang and Liquan Mei",

year = "2005",

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volume = "51",

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journal = "Journal of Engineering Mathematics",

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T1 - Stabilized finite-element method for the stationary Navier-Stokes equations

AU - He, Yinnian

AU - Wang, Aiwen

AU - Mei, Liquan

PY - 2005/4

Y1 - 2005/4

N2 - A stabilized finite-element method for the two-dimensional stationary incompressible Navier-Stokes equations is investigated in this work. A macroelement condition is introduced for constructing the local stabilized formulation of the stationary Navier-Stokes equations. By satisfying this condition, the stability of the Q1 - P0 quadrilateral element and the P1 - P0 triangular element are established. Moreover, the well-posedness and the optimal error estimate of the stabilized finite-element method for the stationary Navier-Stokes equations are obtained. Finally, some numerical tests to confirm the theoretical results of the stabilized finite-element method are provided.

AB - A stabilized finite-element method for the two-dimensional stationary incompressible Navier-Stokes equations is investigated in this work. A macroelement condition is introduced for constructing the local stabilized formulation of the stationary Navier-Stokes equations. By satisfying this condition, the stability of the Q1 - P0 quadrilateral element and the P1 - P0 triangular element are established. Moreover, the well-posedness and the optimal error estimate of the stabilized finite-element method for the stationary Navier-Stokes equations are obtained. Finally, some numerical tests to confirm the theoretical results of the stabilized finite-element method are provided.

KW - Error estimation

KW - Navier-Stokes equations

KW - Stabilized finite element

UR - https://www.scopus.com/pages/publications/20344375713

U2 - 10.1007/s10665-004-3718-5

DO - 10.1007/s10665-004-3718-5

M3 - 文章

AN - SCOPUS:20344375713

SN - 0022-0833

VL - 51

SP - 367

EP - 380

JO - Journal of Engineering Mathematics

JF - Journal of Engineering Mathematics

IS - 4

ER -

Stabilized finite-element method for the stationary Navier-Stokes equations

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Keywords

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