Mixed Finite Element Methods And Numerical Analysis For Parabolic Type Equations

In this paper, a mixed covolume method on triangular grids for psend-parabolic intergo-differential equations and an H~1-Galerkin mixed finite element method for parabolic partial differential equations are considered. By making the numerical approximation and the error analysis, the estimates for them are derived.In Chapter one, we consider the mixed covolume method on triangular grids for the psendparabolic intergo-differential equationsThe analysis of the mixed covolume method of these problems are limited in rectangular grids at present. Meanwhile,the analysis on triangular grids are relatively small. We give the error analysis of semi-discrete and full discrete schemes and derive the optimal rate of convergence for approximate pressure as well as for approximate velocity in L~2-norm.In Chapter two, we study the H~1-Galerkin mixed finite element method for parabolic partial differential problemswhere the coefficients a,b,c are smooth functions of x and t . Compared to the standard procedure .C~1-continuity for the approximating finite dimensionalsubspaces can be relaxed for the proposed method . In the paper ,we give the semidiscrete /^-Galerkin mixed finite element procedure and derive the rate of convergence for approximate pressure as well as for approximate velocity in L2-norm and in Hx-norm .In Chapter three,the superconvergence between the finite element approximations and the Ritz-Sobolev projection of the exact solution of Sobolev type equations is investigated. Superconvergence one order in V for 2 < p < oc, two orders in W1>p for 2 < p < oo, and almost two orders in W1'00 are obtained.