MIXED FINITE ELEMENT METHODS FOR THE SHALLOWWATER EQUATIONS INCLUDING CURRENT AND SILTSEDIMENTATION （Ⅱ）——THE DISCRETE-TIMECASE ALONG CHARACTERISTICS

The mixed finite element(MFE) methods for a shallow water equation systemconsisting of water dynamics equations, silt transport equation, and the equation of bottomtopography change were derived. A fully discrete MFE scheme for the discrete-time alongcharacteristics is presented and error estimates are established. The existence andconvergence of MFE solution of the discrete current velocity, elevation of the bottomtopography, thickness of fluid column, and mass rate of sediment is demonstrated.

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

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. Foundation items: the National Natural Science Foundation of China (10071052, 49776283); the “Plan of Hundred Talents” of Chinese Academy of Sciences; the National Natural Science Foundation of China for Outstanding Young Scientists (40225015); the Beijing Excellent Talent Special Foundation; the Natural Sciences Foundation of Beijing Biographies: LUO Zhen-dong (1958≈)