Unified analysis for stabilized methods of low-order mixed finite elements for stationary Navier-Stokes equations

Gang CHEN;Min-fu FENG;Yin-nian HE

doi:10.1007/s10483-013-1720-9

Applied Mathematics and Mechanics >

2013 , Vol. 34 >Issue 8: 953 - 970

DOI: https://doi.org/10.1007/s10483-013-1720-9

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Unified analysis for stabilized methods of low-order mixed finite elements for stationary Navier-Stokes equations

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1. Department of Mathematics, Sichuan University, Chengdu 610064, P. R. China;
2. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, P. R. China

Online published: 2013-07-15

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Abstract

A unified analysis is presented for the stabilized methods including the pressure projection method and the pressure gradient local projection method of conforming and nonconforming low-order mixed finite elements for the stationary Navier-Stokes equations. The existence and uniqueness of the solution and the optimal error estimates are proved.

Key words： asymptotic convergence; quadratic integer convex programming; stochastic level value approximation; cross-entropy method; Navier-Stokes equation; Ladyzhenskaya-Babu?ska-Brezzi (LBB) condition; low-order finite element; pressure projection method; pressure gradient local projection method

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Gang CHEN;Min-fu FENG;Yin-nian HE . Unified analysis for stabilized methods of low-order mixed finite elements for stationary Navier-Stokes equations[J]. Applied Mathematics and Mechanics, 2013 , 34(8) : 953 -970 . DOI: 10.1007/s10483-013-1720-9

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