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Numerical approximation of an electro-elastic frictional contact problem modeled by hemivariational inequality

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Abstract

In this paper, an electro-elastic frictional contact problem is studied numerically as a hemivariational inequality. Convergence of the Galerkin approximation for the hemivariational inequality is proved, and Céa’s type inequalities are derived for error estimation. The results are applied to the electro-elastic contact problem, and an optimal order error estimate is deduced for linear element approximation. Finally, two numerical examples are reported, providing numerical evidence of the optimal convergence order theoretically predicted.

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Acknowledgements

Ziping Huang was partially supported by the cooperative project of Tongji Zhejiang College and Haiyan County Environmental Protection Bureau with No. Haiyan wupu(2018)-001-2. Wenbin Chen is supported by the National Science Foundation of China (11671098) and partially supported by Shanghai Science and technology research program (19JC1420101). Cheng Wang is supported by the 10 plus 10 project of Tongji University under Grant No. 4260141304/004/010.

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Authors and Affiliations

  1. School of Mathematical Sciences, Tongji University, Shanghai, 200092, China

    Wei Xu, Ziping Huang & Cheng Wang

  2. Tongji Zhejiang College, Jiaxing, 314051, China

    Wei Xu & Ziping Huang

  3. Department of Mathematics, University of Iowa, Iowa City, IA, 52242, USA

    Weimin Han

  4. School of Mathematical Sciences and Shanghai Key Laboratory for Contemporary Applied Mathematics, Fudan University, Shanghai, 200433, China

    Wenbin Chen

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  1. Wei Xu
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  2. Ziping Huang
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  3. Weimin Han
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  4. Wenbin Chen
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  5. Cheng Wang
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Correspondence to Cheng Wang.

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Xu, W., Huang, Z., Han, W. et al. Numerical approximation of an electro-elastic frictional contact problem modeled by hemivariational inequality. Comp. Appl. Math. 39, 265 (2020). https://doi.org/10.1007/s40314-020-01305-5

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  • DOI: https://doi.org/10.1007/s40314-020-01305-5

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