Numerical Simulations For Viscous Incompressible Flow Problem In Two Dimensional Space

In this paper, a characteristic-mixed finite element and a characteristic finite element method are employed to simulate two kinds of viscous incompressible flow problem .By a thorough numerical analysis ,the error estimates are obstained .The paper is devided into three chapters.Chapter one is the introduction.In Chapter two, we consider a characteristic-mixed finite element method for Navier-Stokes' equationsBy using the stream function-voticity formulation of Navier-Stokes' equations,the equations can be translated into a coupled equations consisting of a stream equation and a voticity equation. The stream equation is simulated by mixed finite element for approximating the stream function and the velocity directly and respectively. Since the voticity equation appears to be convection-dominated, it is suitable to use a characteristic finite element method to approximate . Finally, the optimal order error estimates for the stream function ,the voticity function and the velocity field in L2- norms are derived.In Chapter three, we consider a characteristic finite element method for the math-ematic model consisting of the following equations:The governing equations are uniformly convection-dominated. It is especially diffculty to approximate well by using the standard finite element method.In this Chapter , characteric finite element methods are used to approximate the depth of water,the velocity of water and the volumetric sediment . The error estimates between the exact solution and FE solution are proved .