# A Uniform Convergent Petrov-Galerkin method for a Class of Turning Point Problems

```@article{Feng2022AUC,
title={A Uniform Convergent Petrov-Galerkin method for a Class of Turning Point Problems},
author={Li Feng and Zhongyi Huang},
journal={ArXiv},
year={2022},
volume={abs/2208.03965}
}```
• Published 8 August 2022
• Mathematics, Computer Science
• ArXiv
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 ∞ norm and an energy norm when we select the exact solutions to dual problems…

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