Contains Mixed Finite Element Method For Shallow Water Equations Of Sediment Erosion And Deposition

An initial-boundary value problem for a shallow water equation system consisting of water dynamics equations, silt transport equation, and the equation of bottom topography change, and of some boundary and initial conditions is studied in the paper. The existence of its generalized solution, semidiscrete and fully discrete mixed finite element (MFE) solution is discussed, and the error estimates of the semidiscrete MFE solution are derived. The error estimates are optimal. 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 are demonstrated.