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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