文献类型：会议论文

英文题名：Uniform convergence analysis of finite difference approximations on adaptive mesh for general singular perturbed problems

作者：Wang, Antao[1];Sun, Linan[2,3]

第一作者：Wang, Antao

通讯作者：Sun, LA[1];Sun, LA[2]

机构：[1]Henan Police Coll, Zhengzhou 450046, Peoples R China;[2]Henan Univ Econ & Law, Coll Resources & Environm, Zhengzhou 450046, Peoples R China;[3]Henan Univ, Coll Environm & Planning, Kaifeng 475004, Peoples R China

第一机构：Henan Police Coll, Zhengzhou 450046, Peoples R China

通讯机构：[1]corresponding author), Henan Univ Econ & Law, Coll Resources & Environm, Zhengzhou 450046, Peoples R China;[2]corresponding author), Henan Univ, Coll Environm & Planning, Kaifeng 475004, Peoples R China.|[104848]河南财经政法大学资源与环境学院;[10484]河南财经政法大学;

会议论文集：2nd International Conference on Physics, Mathematics and Statistics (ICPMS)

会议日期：MAY 22-24, 2019

会议地点：Hangzhou, PEOPLES R CHINA

语种：英文

外文关键词：Estimation - Finite difference method - Piecewise linear techniques

摘要：In this paper we consider a more general singular perturbation problem, that is, -epsilon u ''(x) - a(x)u'(x) + b(x)u(x) = f(x) (0 < epsilon << 1) on an adaptive grid. The mesh is constructed adaptively by equidistributing a monitor function based on the arc-length of the approximated solutions. Our analysis provide insight into the convergence behaviour on such mesh, and the posterior error estimates of piecewise linear interpolation about the approximate solution is investigated and an epsilon-uniform error estimate for the first-order upwind discretization of general singular perturbed problem is derived at last. We extend the relevant results of the document to a more general case.