A UNIFORM CONVERGENT PETROV-GALERKIN METHOD FOR A CLASS OF TURNING POINT PROBLEMS  

作　　者：Li Feng Zhongyi Huang 

机构地区：[1]Department of Mathematical Sciences,Tsinghua University,Beijing 100084,China

出　　处：《Journal of Computational Mathematics》2024年第5期1356-1379,共24页计算数学（英文）

基　　金：supported by the NSFC(Grant No.12025104).

摘　　要：In this paper,we propose a numerical method for turning point problems in one dimension based on Petrov-Galerkin finite element method(PGFEM).We first give a priori estimate for the turning point problem with a single boundary turning point.Then we use PGFEM to solve it,where test functions are the solutions to piecewise approximate dual problems.We prove that our method has a first-order convergence rate in both L∞h norm and a discrete energy norm when we select the exact solutions to dual problems as test functions.Numerical results show that our scheme is efficient for turning point problems with different types of singularities,and the convergency coincides with our theoretical results.

关 键 词：Turning point problem Petrov-Galerkin finite element method Uniform convergency 

分 类 号：O241.82[理学—计算数学]