包含泥沙冲淤的浅水方程的混合有限元法(Ⅱ)——时间沿特征方向离散的全离散情形

Mixed Finite Element Methods for the Shallow Water Equations Including Current and Silt Sedimentation (Ⅱ)-The Discrete-Time Case Along Characteristics

进一步研究由水动力学方程、泥沙输运方程和河床变化方程组成的浅水方程混合有限元法,给出时间沿特征方向离散的一种全离散格式,并证明全离散的水流速度、床底高度、水体厚度、水中泥沙含量的混合有限元解的存在性和收敛性(误差估计)

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.