Anisotropic Finite Element Method And Applications

In this paper, we focus on the study of the application of the anisotropic finite element methods.We first consider the nonoconforming finite element approximation for the second order variational obstacle problem. By means of the novel techniques, the optimal error estimates are obtained, which are as same as the results of the conventional finite element element methods.Next, using the double set parameter method, we construct a new 12-parameter rectangular plate element. Moreover, the superclose property of this element is proved under the regular meshes by taking advantage of a series of new approaches. But it should be pointed that the consistency error estimate can be got under the anisotropic meshes. The method used here has not been seen in the relative literatures.Finally, we discuss the planar elasticity problem with the pure displacement boundary value problem as the Lame consistant Aby using the anisotropic locking-free rectangular element. Through introducing special approaches, the optimal error estimates of the energy norm and L2-norm are obtained, which are as same as those of the traditional finite element element methods.The highlight of this paper is that we overcome the dificiencies of the conventional finite element methods, i.e., the severe assumptions on the mesh grading, such as the regular assumptions, quasi-uniform assumptions, inverse assumptions, and thus extend the applicable scope of the finite element methods.