The Mixed Finit Elemnt Method Of Some Evolution Equations

In this paper , we consider mixed finit element methods for the initial-boundary value problems of two order hyperbolic equations and linear integro-differential equations of parabolic type , obtain the error estimates of the discrete schemes for this two kinds of problems .In Chapter one , we consider the Expanded Mixed finite element methods for the followling 2nd order hyperbolic problemsThis method expands the standard mixed formulation in the sense that three variable are explixitly treated : the scalar unknwon , its gradient and its flux. Based on this fomulation , expanded mixed finite element approximations of the hyperbolic problems are considered . Optimal order error estimates for the scalar unknwon , its gradient and its flux in L2-norms are obtained for this new mixed formulation . Also , Quasi-optimal order estimates are obtained for the approximations of the the scalar unknwon , its gradient and its flux .In Chapter two, we consider full disceret scheme of mixed finite element methods for the following initial-value problems of linear integro-differential equations of parabolicIn this chapter , we give the error analysis of this full discrete scheme and get optimalerror estimates for the discrete solutions of u and p .