Two Types Of Sobolev Equations Non-coordination Of The H-1-the Galerkin Mixed Finite Element Method

In this paper, We focus on the study of the applications of H~1 -Galerkin mixed finite element method for two kinds of Sobolev equations. For the first one ,the convergence analysis under regular meshes is given with a new element. And for second one, the convergence analysis is carried out under anisotropic meshes, and the superclose property is obtained based on some novel techniques and typical characters of the element itself, At last, the superconvergence is derived through interpolate post-processing techniques.