Numerical Analysis Of Several Kinds Of Partial Differential Equations

In this paper, a characteristic finite element method for some semi-linear reaction-convection-diffusion models and a mixed covolume method on triangular grids for parabolic problems are considered. By making the numerical approximation and the error analysis, optimal order estimates for the two kinds of equations are derived.In Chapter one, we consider the characteristic finite element method for some semi-linear reaction-convection-diffusion equationsThe method not only preserves the simplicity of schemes and the small of thetruncation, but permits the use of larger time steps. By making the numerical analysis, we obtain the optimal error estimates of L2-norm and H1-norm about the unknown function of u, v and w.In Chapter two, we study the mixed covolume method on triangular grids for parabolic problemsThe analyses of the mixed covolume method of these problems are limited in rect-angular grids at present. Meanwhile, the analyses on triangular grids are relatively small. We give the error analyses of semi-discrete and full discrete schemes and derive the optimal rate of convergence for approximate pressure as well as for approximate velocity in L2-norm. We also give the quasi-optimal estimates for approximate pressure in L∞-norm.