Mixed finite element methods for the shallow water equations including current and silt sedimentation (II)—The discrete-time case along characteristics

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.