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A priori error estimates of discontinuous Galerkin methods for a quasi-variational inequality

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Abstract

We study a priori error estimates of discontinuous Galerkin (DG) methods for solving a quasi-variational inequality, which models a frictional contact problem with normal compliance. In Xiao et al. (Numer Funct Anal Optim 39:1248–1264, 2018), several DG methods are applied to solve quasi-variational inequality, but no error analysis is given. In this paper, the unified numerical analysis of these DG methods is established, and they achieve optimal convergence order for linear elements. Two numerical examples are given, and the numerical convergence orders match well with the theoretical prediction.

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Acknowledgements

We thank three anonymous referees for their valuable comments and suggestions, which greatly improve this work.

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Authors and Affiliations

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

    Fei Wang & Sheheryar Shah

  2. Beijing Computational Science Research Center, Beijing, 100193, China

    Wenqiang Xiao

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  1. Fei Wang
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  2. Sheheryar Shah
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  3. Wenqiang Xiao
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Correspondence to Fei Wang.

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Communicated by Rolf Stenberg.

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This work is supported by the National Natural Science Foundation of China (Grant No. 11771350)

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Wang, F., Shah, S. & Xiao, W. A priori error estimates of discontinuous Galerkin methods for a quasi-variational inequality. Bit Numer Math 61, 1005–1022 (2021). https://doi.org/10.1007/s10543-021-00848-1

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