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Discontinuous Galerkin Methods for Hemivariational Inequalities in Contact Mechanics

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Abstract

In this paper, we study discontinuous Galerkin (DG) methods for solving two contact problems. The first problem involves a frictionless normal compliance contact boundary condition, and the second is a bilateral contact problem with friction. These contact problems are modeled by hemivariational inequalities, which consist of non-convex and non-smooth terms. We apply five DG methods to solve the contact problems and establish a priori error estimates for these methods. We prove that the DG schemes achieve optimal convergence order for linear elements. Two examples are presented for numerical evidence of the theoretically predicted convergence order.

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The datasets generated during the current study are available from the corresponding author on reasonable request.

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The code for the current study is available from the corresponding author on reasonable request.

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Acknowledgements

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

Funding

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

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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. College of Mathematics and Systems Science, Xinjiang University, Urumqi, 830046, Xinjiang, China

    Bangmin Wu

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  1. Fei Wang
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Correspondence to Fei Wang.

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Wang, F., Shah, S. & Wu, B. Discontinuous Galerkin Methods for Hemivariational Inequalities in Contact Mechanics. J Sci Comput 95, 87 (2023). https://doi.org/10.1007/s10915-023-02212-7

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