Finite Element Method And Finite Volume Element Method Of Two 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 following boundary value problem for the nonlinear hyperbolic problem with memory:J = [0,T],we consider the Finite Element Method numerical approximation.New initial approximation of ut(0) is taken.Optimal error estimates in Lp for 2 ≤ p ≤ ∞ are established for arbitrary order finite element. One order supercon-vergence in W1,9 for 2 ≤ p ≤ ∞ are demenstrated as well.In chapter two,we consider the Finite Volume Element Methods for nonlinear hyperbolic problem with memory in R1,...