The Analysis And Application Of H~1-Galerkin Mixed Finite Element Method

In the first part of the paper,we consider the Pseudohyperbolic intergo-differrential equationswhich is simulated by H~1-Galerkin mixed finite element method.This method first split the initial problem into a first order system and then propose a nonsymmetric version of a least square method that is an H~1-Galerkin prosedure for the approximating finite dimensional subspace can be relaxed for the proposed method.Moreeover,the approximating finite element space V_h and W_h are allowed to be of differing polynomial degrees.Hence,estimations have been obtained which ditinguish the better approximation properties of V_h and W_h.We obtain the optimal order of convergence theoreticaly.Numerical examples conform the efficiency of our method.In the second part of the paper,we mainly study the effect of numerical integra- tion in H~1-Galerkin mixed finite element method for following parabolic equationAs we all know, the partial differential equations of the finite element method and mixed finite element method are reduced to solving linear algebraic equations,and the final coefficient of linear equations of the calculation must resort to numerical integration.About the effect of numerical integration on the finite method of the elliptic and parabolic equations, there has been some research. This chapter continue to enrich and expand on the methods of theoretical study, and we give the same degree of convergence with the full conditions and get the optimal L~2 and H~1 error estimates.