# 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} }

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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