Mixed finite element methods for the shallow water equations including current and silt sedimentation (I) - The continuous-time case

Applied Mathematics and Mechanics (English Edition)

Volumn 25, Issue 1, 2004, Pages 80-92

  Luo, Zhen Dong ^a,b   Zhu, Jiang ^b   Zeng, Qing Cun ^b   Xie, Zheng Hui ^b  

^a CAPITAL NORMAL UNIVERSITY   (China)

^b INSTITUTE OF ATMOSPHERIC PHYSICS   (China)

Author keywords

Current and silt sedimentation; Error estimate; Mixed finite element method; Shallow water equation

Indexed keywords

BOUNDARY VALUE PROBLEMS; ERRORS; ESTIMATION; FINITE ELEMENT METHOD; SEDIMENTATION; SILT; WATER;

ERROR ESTIMATE; MIXED FINITE ELEMENT METHOD; SHALLOW WATER EQUATION; SILT SEDIMENTATION; WATER DYNAMIC EQUATION;

FLUID DYNAMICS;

EID: 2442663030     PISSN: 02534827     EISSN: None     Source Type: Journal    
DOI: 10.1007/bf02437296     Document Type: Article

References (15)

1. Bermudez 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.
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.
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.
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.
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.
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: Proceedings of the Third International Congress on Industrial and Applied Mathematics[C]. 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. XIN Xiao-kang, LIU Ru-xun, JIANG Bo-cheng. Computational Fluid Dynamics[M]. Changsha: National Defence Science Technical Press, 1989. (in Chinese)
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. LUO Zhen-dong. Theory Bases and Applications of Finite Element and Mixed Finite Element Methods, Evolutions and Applications[M]. Jinan: Shandong Educations Press, 1996. (in Chinese)
15. Brezzi F, Fortin M. Mixed and Hybrid Finite Element Methods[M]. New York, Berlin, Heidelberg: Springer-Verlag, 1991.