The Numerrical Methods Of Two Kinds Of Evolution Equations

In this paper, we consider numerical simulation of two kinds of evolution equations.In Chapter one, we consider the Characteristics-Mixed finite element numerical simulation for the Euler equation for an incompressible fluid with zero viscosity in two dimensions.By two kinds of Characteristics-Mixed finite element: Raviart-Thomas [6] and H(curl；Ω) [8] ,we approximate vorticity function and velocity of the stream field simultaneously, and obtain Z/2-optimal error estimate under the certain condition. In Chapter two, we consider first order generalized difference scheme for linear integro-differential equation.Lp and Wl,p-norm error estimates of the gerneralized elliptic projection u-Rhu and H1 and L2-norm error estimates of utt-(Rhu)tt are made, so we obtain theLp and -norm estimates of u-uh .