Numerical Approximation And Theorical Analysis Of Several Kinds Of Evolution Equations

In this paper, some numerical approximation methods are proposed and analyzed for several kinds of evolution equations.In chapter one,we consider the Finite Element Method numerical approximation for the initial boundary value problem for the nonlinear Burgers equation:in one dimension. We obtain-optimal and optimal estimates under the certainIn chapter two, Finite Volume Element Methods for nonlinear parabolic integrodif-ferential problems are consided:obtained.In chapter three, Generalized Difference Methods(GDM) for two-dimensional vis-coelastic problems are consided:The new initial values are given in the generalized difference scheme, so we obtain optimal error estimates in LP and as well as some superconvergence estimates in between the GDM solution and the generalized Ritz-Volterra projection of the exact solution.