Mixed Finite Element Methods for the Shallow Water Equations Including Current and Silt Sedimentation (Ⅰ)-The Continuous-Time Case

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

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2004 > 25(1): 74-84

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 (Ⅰ)-The Continuous-Time Case[J]. Applied Mathematics and Mechanics, 2004, 25(1): 74-84.

Citation:

PDF( 2786 KB)

Mixed Finite Element Methods for the Shallow Water Equations Including Current and Silt Sedimentation (Ⅰ)-The Continuous-Time Case

Received Date: 2001-08-08
Rev Recd Date: 2003-08-28
Publish Date: 2004-01-15

Abstract

Abstract

An initial-boundary value problem for shallow equation system consisting of water dynamics equations,silt transport equation,the equation of bottom topography change,and of some boundary and initial conditions is studied,the existence of its generalised solution and semidiscrete mixed fuute element(MFE) solution was discussed,and the error estimates of the semidiscrete MFE solution was derived.The error estimates are optimal.
- mixed finite element method,
- shallow water equation,
- error estimate,
- current and silt sedimentation

FullText(HTML)

References(15)

References

[1]	Bermúdez A,Rodríguez 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
[2]	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
[3]	Agoshkov V I,Ovchinnikov E,Quarteroni A,et al.Recent developments in the numerical simulation of shallow water equations Ⅱ:Temporal discretization[J].Math Models Methods Appl Sci,1994,55(4):533—566.
[4]	Agoshkov V I,Quarteroni A,Saleri F.Recent developments in the numerical simulation of shallow water equation Ⅰ:Boundary conditions[J].Appl Numer Math,1994,15(1):175—200. doi: 10.1016/0168-9274(94)00014-X
[5]	Gray W G.A finite element study of tidal flow data for the north sea and English channel[J].Adv Water Res,1989,12(1):143—154. doi: 10.1016/0309-1708(89)90019-5
[6]	Gray W G,Drolet J,Kinnmark I P E.A simulation of tidal flow in the southern part of the north sea and English channel[J].Adv Water Res,1987,10(1):131—137. doi: 10.1016/0309-1708(87)90019-4
[7]	GUO Dong-jian,ZENG Qing-cun,ZHU Jiang,et al.Long-term computational modelling research on river sedimentation and delta evolution[J].Climatic and Environmental Research,1996,1(1):30—37.
[8]	ZENG Qing-cun.Silt sedimentation and relevant engineering problem—an example of natural cybernetics[A].ICIAM95 held in Hamburg,In:Proceeding of the Third International Congress on Industrial and Applied Mathematics,Akademie Verlag,1995,463—487.
[9]	ZHU Jiang,ZENG Qing-cun,GUO Dong-jian,et al.Sensitivity analysis of hydraulic/sediment transport numerical model[J].J Sediment Research,1998,1(2):89—96.
[10]	Adams R A.Sobolev Spaces[M].New York:Academic Press,1975.
[11]	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.
[12]	Girault V,Raviart P A.Finite Element Approximations of the Navier-Stokes Equations[M].Berlin， Heidelberg， New York:Springer-Verlag,1979.
[13]	Ciarlet P G.The Finite Element Method for Elliptic Problems[M].Amsterdam:North-Holland,1978.
[14]	罗振东.有限元混合法理论基础及其应用，发展与应用[M].济南：山东教育出版社，1996.
[15]	Brezzi F,Fortin M.Mixed and Hybrid Finite Element Methods[M].New York,Berlin,Heidelberg:Springer-Verlag,1991.