Stability of a finite element method for 3D exterior stationary Navier-Stokes flows

被引：3
作者：
Deuring, Paul [1 ]
机构：
[1] Univ Littoral, Lab Math Pures & Appl, F-62228 Calais, France
来源：
APPLICATIONS OF MATHEMATICS | 2007年 / 52卷 / 01期
关键词：
stationary incompressible Navier-Stokes flows; exterior domains; stabilized finite element methods; stability estimates; ARTIFICIAL BOUNDARY-CONDITIONS; WEIGHTED SOBOLEV SPACES; UNBOUNDED-DOMAINS; NONZERO VELOCITY; EQUATIONS; INFINITY; OSEEN;
D O I：
10.1007/s10492-007-0003-8
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider numerical approximations of stationary incompressible Navier-Stokes flows in 3D exterior domains, with nonzero velocity at infinity. It is shown that a P1-P1 stabilized finite element method proposed by C. Rebollo: A term by term stabilization algorithm for finite element solution of incompressible flow problems, Numer. Math. 79 (1998), 283-319, is stable when applied to a Navier-Stokes flow in a truncated exterior domain with a pointwise boundary condition on the artificial boundary.
引用
收藏
页码：59 / 94
页数：36
相关论文
共 51 条
[1]  
Adams R. A., 2003, Sobolev Spaces
[2]  
ALOUGES F, 2003, METHODS PARTIAL DIFF, V19, P592
[3]  
BABENKO KI, 1973, PMM-J APPL MATH MEC, V37, P651, DOI DOI 10.1016/0021-8928(73)90115-9
[4]   Adaptive boundary conditions for exterior flow problems [J].
Bönisch, S ;
Heuveline, V ;
Wittwer, P .
JOURNAL OF MATHEMATICAL FLUID MECHANICS, 2005, 7 (01) :85-107
[5]  
Brenner S.C., 2002, Texts in Applied Mathematics, Vsecond
[6]  
Brezzi F., 2012, Mixed and Hybrid Finite Element Methods
[7]   New efficient boundary conditions for incompressible Navier-Stokes equations: A well-posedness result [J].
Bruneau, CH ;
Fabrie, P .
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 1996, 30 (07) :815-840
[8]   Boundary conditions on artificial frontiers for incompressible and compressible Navier-Stokes equations [J].
Bruneau, CH .
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2000, 34 (02) :303-314
[9]   A preconditioner for generalized saddle point problems: Application to 3D stationary Navier-Stokes equations [J].
Calgaro, C. ;
Deuring, P. ;
Jennequin, D. .
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2006, 22 (06) :1289-1313
[10]   Exterior stationary Navier-Stokes flows in 3D with nonzero velocity at infinity: Asymptotic behavior of the second derivatives of the velocity [J].
Deuring, P .
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2005, 30 (07) :987-1020
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