For Sobolev Equation The Anisotropy Of H ~ 1-galerkin Method

In this paper, we focus on the study of the applications of H~1—Galerkin mixed finite element of sobolev equations on anisotropic meshes. At first, We consider the case when the two approximation spaces are nonconforming finite elements, the error estimates of the new mixed finite element are presented without requiring the Ritz projection. Next, we study the case when the approximation spaces are the anisotropic bilinear element and a conforming Bernadi—Rangel element on anisotropic meshes. The error estimates are obtained, which are the same as those of the traditional methods. Thus the results of this paper extend the applicable scope of the mixed finite element methods.