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Virtual Element Method for a History-Dependent Variational-Hemivariational Inequality in Contact Problems

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Abstract

In this paper, numerical analysis is carried out for a class of history-dependent variational-hemivariational inequalities arising in contact problems. A fully discrete scheme is introduced for the inequality problem, in which the history-dependent operator is approximated by the trapezoidal rule and the spatial variable is approximated by the lowest-order virtual element method. An optimal order error estimate is derived under appropriate solution regularity assumptions. Numerical examples are presented to illustrate the theoretical results.

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Acknowledgements

We thank the two anonymous referees for their valuable comments and suggestions.

Funding

The work of Min Ling was partially supported by China Postdoctoral Science Foundation (Grant No. 2022M720262).

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  1. School of Mathematical Sciences, Peking University, Beijing, 100871, China

    Wenqiang Xiao & Min Ling

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  1. Wenqiang Xiao
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Xiao, W., Ling, M. Virtual Element Method for a History-Dependent Variational-Hemivariational Inequality in Contact Problems. J Sci Comput 96, 82 (2023). https://doi.org/10.1007/s10915-023-02310-6

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