The error analysis and the improved algorithms for the infinite element method

Abstract

This paper is concerned with the theoretical analysis and the practiccal algorithms for the infinite element method which was developed in recent years. With the aid of the inequalities related to the Sobolev space given in the paper, the error estimates in the norms of (with weight), and and , the estimates like superconvergence and so on are comprehensively investigated for the method. Many of the conclusions obtained are optimal or nearly optimal. Also, some relative algorithms are analyzed and improved and the results are suported by numerical experiments