| In this paper, we first focus on two new anisotropic nonconforming mixed finite element formulations for solving Stokes problem in 3-D. By introducing the special novel approaches, the optimal error estimates are obtained. With the advantages of simple structure and fewer degrees of freedom, the above two elements are considered to be comparatively ideal finite elements in 3-D up to now.Second, we study the planar elasticity problem with the pure displacement boundary value problem by nonconforming anisotropic Crouzeix-Raviart triangular element. It is shown that this element is Locking-free on anisotropic meshes. At the same time, by introducing special novel approaches, the optimal error estimates of energy norm and L~2- norm are obtained, which are as same as that of the traditional finite element methods. Thus we get rid of the restrictions of the regularity assumption and quasi-uniform assumption required on the meshes in the conventional finite element methods analysis, and extend the application scope of nonconforming finite elements. |
