Finite Element For Singular Two-point Boundary Value Problem

Finite element method is an effective method to find the numerical solution of differential equation,but in practice,the finite element solution tends to conver-gence slowly or diverge,and the precision can not reach the expected effect.To improve the accuracy of the solution,we superconvergence analysis for a class of singular two-point boundary value problems.The first part is introduction and preliminary knowledge,the background and research status of the problem,the history and present situation of superconver-gence of finite element and the related definition and properties of Sobolev space in this paper.The second part mainly introduces the approximation properties of the finite element solution of the linear problem and the approximation properties of the fi-nite element of the nonlinear problem.Through the interpolation postprocessing,the whole superconvergence result is obtained:In the third part,the results of error analysis are verified by numerical experiments.