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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

罗振东 朱江 曾庆存 谢正辉

罗振东, 朱江, 曾庆存, 谢正辉. 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.
引用本文: 罗振东, 朱江, 曾庆存, 谢正辉. 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.
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: 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.

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

基金项目: 国家自然科学基金(10071052,49776283);国家杰出青年基金(40225015);中国科学院“百人计划”资助项目;北京市优秀人才专项经费资助项目;中国科学院九五重点项目资助项目(K2952-51-434)
详细信息
    作者简介:

    罗振东(1958- ),男,广西桂平人,教授,博士,博士生导师(联系人.Tel:86-10-68239661;E-mail:luozhd@mail.cnu.edu.cn);曾庆存(1935- ),男,研究员,中科院院士,博士,博导.

  • 中图分类号: O241.4

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

  • 摘要: 研究由水动力方程、 泥沙输运方程和河床变化方程组成的浅水方程的初边值问题, 讨论其广义解和混合有限元解的存在性, 并导出半离散混合有限元解的误差估计, 这些估计是最优阶的.
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    [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.
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    [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
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    [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.
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出版历程
  • 收稿日期:  2001-08-08
  • 修回日期:  2003-08-28
  • 刊出日期:  2004-01-15

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