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Optimal Order of Uniform Convergence for Finite Element Method on Bakhvalov-Type Meshes

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Abstract

We propose a new analysis of convergence for a kth order (\(k\ge 1\)) finite element method, which is applied on Bakhvalov-type meshes to a singularly perturbed two-point boundary value problem. A novel interpolant is introduced, which has a simple structure and is easy to generalize. By means of this interpolant, we prove an optimal order of uniform convergence with respect to the perturbation parameter. Numerical experiments illustrate these theoretical results.

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Acknowledgements

We thank the two anonymous referees for their valuable comments and suggestions that led us to improve this paper.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, China

    Jin Zhang

  2. School of Mathematics and Statistics, Qilu University of Technology (Shandong Academy of Sciences), Jinan, 250353, China

    Xiaowei Liu

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  1. Jin Zhang
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  2. Xiaowei Liu
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Correspondence to Jin Zhang.

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This research is supported by National Natural Science Foundation of China (11771257, 11601251), Shandong Provincial Natural Science Foundation, China (ZR2017MA003).

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Zhang, J., Liu, X. Optimal Order of Uniform Convergence for Finite Element Method on Bakhvalov-Type Meshes. J Sci Comput 85, 2 (2020). https://doi.org/10.1007/s10915-020-01312-y

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  • DOI: https://doi.org/10.1007/s10915-020-01312-y

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