Mixed Finite Element Methods for the Shallow Water Equations Including Current and Silt Sedimentation (Ⅱ)-The Discrete-Time Case Along Characteristics

LUO Zhen-dong; ZHU Jiang; ZENG Qing-cun; XIE Zheng-hui

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Article Navigation > Applied Mathematics and Mechanics > 2004 > 25(2): 166-180

LUO Zhen-dong, ZHU Jiang, ZENG Qing-cun, XIE Zheng-hui. Mixed Finite Element Methods for the Shallow Water Equations Including Current and Silt Sedimentation (Ⅱ)-The Discrete-Time Case Along Characteristics[J]. Applied Mathematics and Mechanics, 2004, 25(2): 166-180.

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Mixed Finite Element Methods for the Shallow Water Equations Including Current and Silt Sedimentation (Ⅱ)-The Discrete-Time Case Along Characteristics

Received Date: 2000-08-30
Rev Recd Date: 2003-06-28
Publish Date: 2004-02-15

Abstract

Abstract

The mixed finite element(MFE)methods for a shallow water equation system consisting of water dynamics equations,silt transport equation,and the equation of bottom topography change were derived.A fully discrete MFE scheme for the discrete-time along characteristics is presented and error estimates are established.The existence and convergence of MFE solution of the discrete current velocity,elevation of the bottom topography,thickness of fluid column,and mass rate of sediment is demonstrated.
- mixed finite element method,
- shallow water equation,
- error estimate,
- current and silt sedimentation,
- characteristics method

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References(12)

References

[1]	Boris J P,Book D L.Flux corrected transport[J].SHASTA J Comput Phys,1973,2(1):36—69.
[2]	Pironneau O.On the transport-diffusion algorithm and its applications to the Navier-Stokes equations[J].Numer Math,1982,38(2):309—332. doi: 10.1007/BF01396435
[3]	Bermúdez A,Rodriguez′ C,Vilar M A.Solving shallow water equations by a mixed implicit finite element method[J].IMA J Numer Anal,1991,11(1):79—97. doi: 10.1093/imanum/11.1.79
[4]	罗振东，朱江，曾庆存，等.包含泥沙冲淤的浅水方程的混合有限元法(Ⅰ)——时间连续的情形[J].应用数学和力学，2004，25(1)：74—84.
[5]	忻孝康，刘儒勋，蒋伯诚.计算流体动力学[M].长沙：国防科技大学出版社，1989.
[6]	ZENG Qing-cun.Silt sedimentation and relevant engineering problem—an example of natural cybernetics[A].In:Proceeding of the Third International Congress on Industrial and Applied Mathematics[C].ICIAM95 held in Hamburg,Academic Verlag,1995,463—487.
[7]	Chipada S,Dawson C N,Martinez M L,et al.Finite element approximations to the system of shallow water equations—Ⅰ:Continuous-time a priori error estimates[J].SIAM J Numer Anal,1998,35(2):692—711. doi: 10.1137/S0036142995296515
[8]	Adams R A.Sobolev Spaces[M].New York:Academic Press,1975.
[9]	Ciarlet P G.The Finite Element Method for Elliptic Problems[M].Amsterdam:North-Holland,1978.
[10]	罗振东.有限元混合法理论基础及其应用[M].济南：山东教育出版社，1996.
[11]	Brezzi F,Fortin M.Mixed and Hybrid Finite Element Methods[M].Berlin,Heidelberg,New York:Springer-Verlag,1991.
[12]	Girault V,Raviart P A.Finite Element Approximations of the Navier-Stokes Equations[M].Berlin Beidelberg, New York:Springer-Verlag,1979.