The Conjugate Gradient Method and Block Iterative Method for Penalty Finite Element of Three-Dimensional Navier-Stokes Equations

Li Kai-tai; Huang Ai-xiang; Li Du; Liu Zhi-xing

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Article Navigation > Applied Mathematics and Mechanics > 1983 > 4(6): 821-834

Li Kai-tai, Huang Ai-xiang, Li Du, Liu Zhi-xing. The Conjugate Gradient Method and Block Iterative Method for Penalty Finite Element of Three-Dimensional Navier-Stokes Equations[J]. Applied Mathematics and Mechanics, 1983, 4(6): 821-834.

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The Conjugate Gradient Method and Block Iterative Method for Penalty Finite Element of Three-Dimensional Navier-Stokes Equations

Xi'an Jiaotong University, Xi'an

Received Date: 1982-12-12
Publish Date: 1983-12-15

Abstract

Abstract

A conjugate gradient and block iterative algorithm for element solution of penalty variational form of Navier-Stokes equations are presented. Because the algorithm of solving single variable minimizing problem is simplified, the computing time is greatly saved.In this paper numerical examples are also provided.

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References(15)

References

[1]	李开泰、黄艾香、马逸尘、李笃、刘之行.Navier-Stokes问题加罚变分形式的最优控制有限元逼近.西安交通大学学报,16. 1(1982). 85-88.
[2]	李笃,三维Navier-Stukes问题的共扼梯度法及数值试验.西安交通大学学报,16, 4 (1982),81-90.
[3]	刘之行,三维Navier-Stokes问题加罚变分形式的分块迭代法及其应用程序,西安交通大学学报,16,4 (1982). 91-102.
[4]	Bristeau,M.O.,O.Pironneau,R.Glowinski,J.Periaux and P.Perrier,On the numerical solution of nonlinear problems in fluid dynamics by least squares and finite element methods (I):Least square formulation and conjugate gradient solution of the continuous problems,Comp.Math.Appl.Mech.Eng.(17)/(18),(1979),619-657.
[5]	Giraut,V.,and P.A.Raviart,Finite Element Approximation for the Navier-Stokes Equations,Lecture Notes in Mathematics,Vol.749,Springer-Verlag,Berlin,(1980).
[6]	Teman,R.,Navier-Stokes Equations,North-Holland,Amsterdam,(1977).
[7]	Reddy,J.N.,On the Mathematical Theory of the Penalty-Finite Elements for Navier-Stokes Equations,Proceedings of the Third International Conference onFinite Elements in Flow Problems,Vol.2,(1980)
[8]	Zienkiewicz,O.C.,Constrained Variational Principles and Penalty Function Methods in Finite Element Analysis,Lecture Notes in Mathematics,P.363(Edited by Dald and B.B.Eckman),Springer-Verlag,New York,(1974).
[9]	Falk,R.S.,and J.T.King,A penalty and extrapolation method for the stationary Stokes equations,SIAM.J.Numer.Anal 13(1979),814-829.
[10]	Bercoviex,M.,and M.Engelman,A finite element for the numerical solution of viscous incompressible flows,J.Comp.Phys.30(1979),181-201.
[11]	Hughes,T.J.R.,W.K.Liu and A.Brooks,Finite element analysis of incompressible viscous flows by the penalty function formulation,J.Comp.Phys.,30(1979) 1-60.
[12]	Song,Y.J.,J,T.Oden and N.Kikuchi,Discrete LBB-Conditions for RIP-Finite Element Methods,TICON Report,80-7(1980).
[13]	Oden,J.T.,RIP-Methods for Stokesian Flows,Finite Elements in Fluids,Vol.4,John Wiley Sons.
[14]	Oden,J.T.,Penalty Methods and Selective Reduced Integration for Stokesian Flow,Proceedings of the Third International Conference on Finite Elements in Flow Problems,Banff.Alberta,Canada,(1980),140-145.
[15]	Oden,J.T.,Penalty Finite Element Methods for Constrained Problems in Elasticity,Symposium on Finite Element Methods,Hefei, Anhui, China (1981).