Superconvergence Analysis For The Mixed Finite Element Methods Of The Two Class Elliptic Problems

In this paper, we focus on superconvergence analysis for the mixed finite element methods of the two class elliptic problems. Firstly, a conforming finite element and a nonconforming finite element schemes of Possion equations are persented based on a new mixed variational form, then the weak coercivity of this form is established. Furthermore, through integral identity techniques the superclose properties of the related variables are derived under anisotropic meshes. At the same time, the global superconvergence is ob-tained by constructing the interpolation post-processing operator.Secondly, we present the supercloseness property of the stable rectangular mixed finite elements for the stress-displacement system derived from the Hilliger-Reissner variational principle of the plane elasticity problem. Then, the global superconvergence result of the displacement field is established by employing Clement interpolation and an appropriate postprocessing technique.Lastly, an optimally consistent stabilization for the plane elasticity problem is ana-lyzed, then the superclose properties of the related variables about the bilinear element are derived on uniform meshes.