Error estimates of finite element method about elliptic problems with singular righthand side

摘要

In this paper, on basis of other related works (see [R. Scott, Optimal L∞ estimates for the finite element method on irregular meshes, Math. Comp. V 30 (1976) 681–697; Qun Lin, Qi-ding Zhu, The Preprocessing and Postprocessing for FEM, Shanghai Science Press, China, 1994; I. Babuska, A. Miller, The post-processing in the finite element method, Parts I–II, Internat. J. Numer. Methods Engrg. 20 (1984) 1085–1109, 1111–1129]), we will continue to study the theory of FEM for elliptic problems with singular righthand side. The main difference between this paper and other related works (see Scott, 1976; Lin and Zhu, 1994; Babuska and Miller, 1984) is that it will present some local estimates for FEM of elliptic problems with singular righthand side. Of course, some numerical examples will be given to investigate those error estimates.