Subconvergence And A Self-Adaptive Posteriori Error Estimates Of Bilinear Finite Element

In this thesis, we study the problem about subconvergence and a self-adaptive posteriori error estimates of bilinear finite element.Even for the problem with singularity, we can obtain a globe accuracy results of finite element with the less calculation and quicker speed using the method given in our paper. This paper is arranged specificly as follows:In Chapter 1, we mainly provide some backgroud information and meaning about our research and the statement of our main results that we have already obtain.In Chapter 2, we mainly introduce some basic concepts and properties of finite element, which would appear in our next chapters.In Chapter 3, we propose a posteriori error estimator and proved theoretically that this criterion can be the standard of distinguishing the subconvergence units.In Chapter 4, we prove the self-adaptive property of posteriori error estimator defined by ourself.In Chapter 5, We explain by several examples that we only need locally refine the bad elements, and the globe accuracy results of finite element can be raised with the minimal workload and the quickest speed.In the last chapter, we generalize this paper and prospect the related problem about this paper.