Galerkin Approximation Of Green's Function Estimation And Its Applications

This paper concerns about the quality of quasi-Green 's Function for the second order elliptic problems. Using weighted norm method, the paper obtains a new estimate for Galerkin approximation of quasi-Green Function and gives a directed and brief proof for existed superconvergence conclusion.The paper is divided into five parts:Part One: Introduction. It summarizes the two current superconvergence theory, one is proposed by Cornell school, the other is proposed by China;Part Two: The quasi-Green's Function and its quality;Part Three: Weighted norm and some lemma about it. In this part, author introduces weighted-function:and expounds the quality of the weighted norm; Part Four: Estimate for Galerkin approximation of quasi-Green's Function by using weighted norm method. This part,using weighted norm theory obtains a new estimate; Part Five: Application.