Uzawa Type Algorithm Based on Dual Mixed Variational Formulation

WANG Guang-hui; WANG Lie-heng

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Article Navigation > Applied Mathematics and Mechanics > 2002 > 23(7): 682-688

WANG Guang-hui, WANG Lie-heng. Uzawa Type Algorithm Based on Dual Mixed Variational Formulation[J]. Applied Mathematics and Mechanics, 2002, 23(7): 682-688.

Citation:

WANG Guang-hui, WANG Lie-heng. Uzawa Type Algorithm Based on Dual Mixed Variational Formulation[J]. Applied Mathematics and Mechanics, 2002, 23(7): 682-688.

Citation:

WANG Guang-hui, WANG Lie-heng. Uzawa Type Algorithm Based on Dual Mixed Variational Formulation[J]. Applied Mathematics and Mechanics, 2002, 23(7): 682-688.

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Uzawa Type Algorithm Based on Dual Mixed Variational Formulation

WANG Guang-hui¹,
WANG Lie-heng²

1.
State Key Laboratory of Acoustics, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100080, P R China;
2.
State Key Laboratory of Scientific/Engineering Computing, Institute of Computational Mathem atics a nd Scientific/Engineering Computing, Chinese Academy of Sciences, Beijing 100080, P R China

Received Date: 2001-08-16
Rev Recd Date: 2002-03-18
Publish Date: 2002-07-15

Abstract

Abstract

Based on the dual mixed variational formulation with three variants (stress, displacement, displacement on contact boundary) and the unilateral beaming problem of finite element discretization, an Uzawa type iterative algorithm is presented. The convergence of this iterative algorithm is proved, and then the efficiency of the algorithm is tested by a numerical example.
- contact problem in elasticity,
- unilateral beaming problem,
- dual mixed variational formulation,
- Raviart-Thomas element,
- Uzawa algorithm

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References(7)

References

[1]	王烈衡,王光辉.弹性接触问题的一种新的混合变分形式[J].计算数学,1999,21(2):237-244.
[2]	王烈衡,王光辉.弹性接触问题的对偶混合有限元分析[J].计算数学,1999,21(4):483-494.
[3]	Glowinski R,Lions J,Tnemolieres R.Numerical Analysis of Variational Inequalities[M].Amsterdam,New York,Oxford:North-Holland,1981.
[4]	Kikuchi N,Oden J T.Contact Problems in Elasticity:A Study of Variational Inequalities and Finite Element Methods[M].Siam Philadelphia,1988.
[5]	Admas D A.Sobolev Space[M].New York:Academic Press,1975.
[6]	Ciarlet P G.The Finite Element Method for Elliptic Problems[M].Amsterdam,New York,Oxford:North Holland,1978.
[7]	Brezzi F,Fortin M.Mixed and Hybrid Finite Element Methods[M].New York:Springer-Verlag,1991