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Numerical Studies of a Class of Thermoviscoelastic Frictional Contact Problem Described by Fractional Differential Hemivariational Inequalities

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Abstract

The intention of our study is to investigate a thermoviscoelastic frictional contact problem involving time-fractional order operators and long memory effects. Both the Kelvin–Voigt constitutive law and the heat conduction equation incorporate time-fractional characteristics. The model’s variational formulation yields a coupled system consisting of a history-dependent hemivariational inequality governing the displacement field along with an evolution equation describing the temperature field. The existence of a unique weak solution is established by using Banach fixed point theory and some results on hemivariational inequalities. Subsequently, we present a fully discretized scheme and pay attention to the derivation of error estimates for the numerical solutions. The attainment of an optimal order error estimate is achieved under a few solution regularity assumptions. Numerical simulations are conducted at the end of this manuscript to validate our theoretical findings.

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Acknowledgements

We would like to thank the reviewers and the editors for their insightful comments and suggestions, which greatly improved the quality of this manuscript.

Funding

The work of Hailing Xuan is supported by the Natural Science Foundation of Zhejiang Province (No. LQ24A010002), while the work of Lele Yuan is supported by the Natural Science Foundation of Shandong Province (No. K21LB24).

Author information

Authors and Affiliations

  1. College of Mathematics and Computer Science, Zhejiang A&F University, Hangzhou, 311300, People’s Republic of China

    Hailing Xuan

  2. School of Mathematical Sciences, Zhejiang University, Hangzhou, 310027, People’s Republic of China

    Xiaoliang Cheng

  3. School of Mathematical Sciences, Liaocheng University, Liaocheng, 252000, People’s Republic of China

    Lele Yuan

Authors
  1. Hailing Xuan
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  2. Xiaoliang Cheng
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  3. Lele Yuan
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Contributions

Hailing Xuan: Writing-review & editing, Writing-original draft, Validation, Methodology, Investigation. Xiaoliang Cheng: Writing-review & editing, Validation, Supervision, Investigation. Lele Yuan: Writing-review & editing, Writing-original draft, Validation, Investigation.

Corresponding author

Correspondence to Lele Yuan.

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Xuan, H., Cheng, X. & Yuan, L. Numerical Studies of a Class of Thermoviscoelastic Frictional Contact Problem Described by Fractional Differential Hemivariational Inequalities. J Sci Comput 103, 4 (2025). https://doi.org/10.1007/s10915-025-02815-2

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  • DOI: https://doi.org/10.1007/s10915-025-02815-2

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