Applied Mathematics and Mechanics

, Volume 25, Issue 2, pp 186–201

# 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
Article

## 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.

### Key words

mixed finite element method shallow water equation error estimate current and silt sedimentation characteristics method

O241.4

### 2000 Mathematics Subject Classification

65N30 35Q10 65M30

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© Editorial Committee of Applied Mathematics and Mechanics 2004

## Authors and Affiliations

• Luo Zhen-dong
• 1
• 2
• Zhu Jiang
• 2
• Zeng Qing-cun
• 2
• Xie Zheng-hui
• 2
1. 1.Department of MathematicsCapital Normal UniversityBeijingP. R. China
2. 2.Institute of Atmospheric PhysicsChinese Academy of SciencesBeijingP. R. China