The Mixed Finite Element Method And Numerical Analysis For Two Kinds Of Parabolic Partial Differential Equations

In this paper, a characteristics-mixed finite element method for some semi-linear reaction-convection-diffusion models and a mixed covolume method on rectangular grids for quasi-linear parabolic integro-differential equation arc considered. By making the numerical approximation and the error analysis, optimal order estimates in L~2- norm of the solusions of these schemes are derived.In Chapter one, we consider the characteristics-mixed finite element method for some semi-linear reaction-convection-diffusion equationsThe new method is a combination of characteristic approximation to handle the conveetion part, to ensure the high stability of the method in approximating the sharp fronts and reduce the numerical diffusion, a smaller timer truncation is gained at the same time, and a mixed finite element spatial approximation to deal with the diffusion part, the scaler unkown and the adjoint veetor function are approximated optimally and simultaneously.In Chapter two, we consider the mixed covolume method for the parabolic integrodifferential equation In this chapter, the analyses of the mixed covolume method of these problems are limited on rectangular grids at present. Meanwhile, the analyses on rectangular grids are relatively small. We give the mixed covolume elliptic projections (??) of this problem and their optimal order error estimates in L~2 or H(div): (?)-u, ((?)- u)_t, ((?)- u)_u, (?)-p, ((?)-p)_t, ((?)-p)_u. In the rest part of this chapter, by making the numerical approximation and the error analysis, optimal order error estimates for the scaler unknown and the adjoint vector function in L~2-norms and H(div)-norms are obtained.