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A Posteriori Error Estimates of Virtual Element Method for a Simplified Friction Problem

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Abstract

We study a posteriori error analysis of the virtual element method (VEM) for a simplified friction problem, which is a representative elliptic variational inequality of the second kind. By treating hanging nodes as vertices of polygonal elements, the virtual element method does not require any local mesh post-processing after the adaptive mesh refinement. In this work, residual type error estimators are derived for designing adaptive VEM to solve the simplified friction problem. Furthermore, the reliability and efficiency of the error estimators are proved. Finally, a numerical example is given to verify the theoretical results.

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Acknowledgements

We thank the two anonymous referees for their valuable comments and suggestions, which significantly improve this work.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, Shaanxi, People’s Republic of China

    Yanling Deng & Fei Wang

  2. Hunan Key Laboratory for Computation and Simulation in Science and Engineering, School of Mathematics and Computational Science, Xiangtan University, Xiangtan, 411105, Hunan, People’s Republic of China

    Huayi Wei

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  1. Yanling Deng
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  2. Fei Wang
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Correspondence to Fei Wang.

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The work of this author (Fei Wang) was partially supported by the National Natural Science Foundation of China (Grant No. 11771350). The work of this author (Huayi Wei) was partially supported by the National Natural Science Foundation of China (Grant No. 11871413).

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Deng, Y., Wang, F. & Wei, H. A Posteriori Error Estimates of Virtual Element Method for a Simplified Friction Problem. J Sci Comput 83, 52 (2020). https://doi.org/10.1007/s10915-020-01242-9

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  • DOI: https://doi.org/10.1007/s10915-020-01242-9

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