Stabilized finite element method for the non-stationary navier-stokes problem

H. E. Yinnian; Yanping Lin; Weiwei Sun

doi:10.3934/dcdsb.2006.6.41

Stabilized finite element method for the non-stationary navier-stokes problem

H. E. Yinnian
, Yanping Lin
, Weiwei Sun

Department of Mathematics

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

45 Citations (Scopus)

Abstract

In this article, a locally stabilized finite element formulation of the two-dimensional Navier-Stokes problem is used. A macroelement condition which provides the stability of the Q₁ -P₀ quadrilateral element and the P₁ -P₀ triangular element is introduced. Moreover, the H¹ and L²-error estimates of optimal order for finite element solution (u_h,p_h,) are analyzed. Finally, a uniform H¹ and L²-error estimates of optimal order for finite element solution (u_h, p_h) is obtained if the uniqueness condition is satisfied.

Original language	English
Pages (from-to)	41-68
Journal	Discrete and Continuous Dynamical Systems - Series B
Volume	6
Issue number	1
DOIs	https://doi.org/10.3934/dcdsb.2006.6.41
Publication status	Published - Jan 2006

Research Keywords

Navier-stokes problem
Stabilized finite element
Uniform error estimate

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abstract = "In this article, a locally stabilized finite element formulation of the two-dimensional Navier-Stokes problem is used. A macroelement condition which provides the stability of the Q1 -P0 quadrilateral element and the P1 -P0 triangular element is introduced. Moreover, the H1 and L2-error estimates of optimal order for finite element solution (uh,ph,) are analyzed. Finally, a uniform H1 and L2-error estimates of optimal order for finite element solution (uh, ph) is obtained if the uniqueness condition is satisfied.",

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AU - Yinnian, H. E.

AU - Lin, Yanping

AU - Sun, Weiwei

PY - 2006/1

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N2 - In this article, a locally stabilized finite element formulation of the two-dimensional Navier-Stokes problem is used. A macroelement condition which provides the stability of the Q1 -P0 quadrilateral element and the P1 -P0 triangular element is introduced. Moreover, the H1 and L2-error estimates of optimal order for finite element solution (uh,ph,) are analyzed. Finally, a uniform H1 and L2-error estimates of optimal order for finite element solution (uh, ph) is obtained if the uniqueness condition is satisfied.

AB - In this article, a locally stabilized finite element formulation of the two-dimensional Navier-Stokes problem is used. A macroelement condition which provides the stability of the Q1 -P0 quadrilateral element and the P1 -P0 triangular element is introduced. Moreover, the H1 and L2-error estimates of optimal order for finite element solution (uh,ph,) are analyzed. Finally, a uniform H1 and L2-error estimates of optimal order for finite element solution (uh, ph) is obtained if the uniqueness condition is satisfied.

KW - Navier-stokes problem

KW - Stabilized finite element

KW - Uniform error estimate

UR - https://www.scopus.com/pages/publications/33644509559

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U2 - 10.3934/dcdsb.2006.6.41

DO - 10.3934/dcdsb.2006.6.41

M3 - RGC 21 - Publication in refereed journal

SN - 1531-3492

VL - 6

SP - 41

EP - 68

JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

IS - 1

ER -

Stabilized finite element method for the non-stationary navier-stokes problem

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Research Keywords

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