Maximum Norm A Posteriori Error Estimates For A Class Of Singularly Perturbed Problem

In this paper we first use the comparison principle and the Green’s function to analyze the stability of the continuous problem. Then we construct a discrete scheme, and discuss the maximum norm a posterior error estimates of the piecewise linear interpolation and the piecewise quadratic interpolation of the numerical solution.In Chapter one, we introduce the background and progress of the singular perturbation problem, and give the research questions, main results and we give some basic knowledge that will be used in this thesisIn Chapter two. we mainly study the stability of the continuous problems and discuss the posterior error estimates of the piecewise linear interpolation and the piecewise quadratic interpolation of the approximate solution;In Chapter three, we summarize the main results of this thesis and the future direction of the main research.