Coupling Methods With A Class Of Nonconforming Finite Elements And Some Researches On Hermite-type Anisotropic Mixed Finite Elements

In this paper,the second order elliptic problem is studied firstly by using conforming finite element and nonconforming finite element in the different part of the area respectively. Convergence of this coupling method is given by using some novel approaches;Then a new unconventional anisotropic Hermite-type rectangular element is constructed and a mixed finite element scheme is proposed for the second order elliptic problem. Based on bubble function technique a simplified and stabilized mixed element formulation for the above problem is also constructed. The convergence analysis and posteriori estimates of this formulation are given.