Superconvergence Of The Finite Element Method For Green's Function

The finite element method is highly efficient numerical method for solving differential equations and the superconvergence plays an important role in improving the accuracy of the finite element method. Therefore, the theory about that has become very important and even necessary. Currently, the references about the finite element study of super-convergence literature are quite a lot. For example, Super-convergence of two-dimensional finite element elliptic problems conducted extensive research; two-dimensional numerical solution of elliptic problems and Green's function method for a finite element analysis is also carried out many studies. However, we are rarely seen the references investigating the superconvergence of the finite element method for Green's function. Based on this, the paper shall discuss the problem. This paper has studied Super-convergence of the finite element method for Green's function. The main research work can be summarized as the following two aspects:Firstly, combining the solution of the super-convergence of one-order element for the common second-order elliptic equations with the solution of pointwise error estimates at any point of the bilinear element of the Green's function. In this paper, I have examined the super-convergence of this kind of problem at any point of the bilinear rectangular element of the Green's function in detail. And I have got the pointwise error estimates.Secondly, I have studied the numerical solution of the three-dimensional Poisson equation at any point of the local convergence and got some super-convergence results on the displacement.