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April  2021, 20(4): 1521-1543. doi: 10.3934/cpaa.2021031

## Numerical analysis of a thermal frictional contact problem with long memory

 School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China

* Corresponding author

Received  October 2020 Revised  January 2021 Published  March 2021

Fund Project: This work was supported by the European Union's Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie Grand Agreement No. 823731 CONMECH and Major Scientifc Research Project of Zhejiang Lab No. 2019DB0ZX01

The objective in this paper is to study a thermal frictional contact model. The deformable body consists of a viscoelastic material and the process is assumed to be dynamic. It is assumed that the material behaves in accordance with Kelvin-Voigt constitutive law and the thermal effect is added. The variational formulation of the model leads to a coupled system including a history-dependent hemivariational inequality for the displacement field and an evolution equation for the temperature field. In study of this system, we first consider a fully discrete scheme of it and then focus on deriving error estimates for numerical solutions. Under appropriate assumptions of solution regularity, an optimal order error estimate is obtained. At the end of this manuscript, we report some numerical simulation results for the contact problem so as to verify the theoretical results.

Citation: Hailing Xuan, Xiaoliang Cheng. Numerical analysis of a thermal frictional contact problem with long memory. Communications on Pure & Applied Analysis, 2021, 20 (4) : 1521-1543. doi: 10.3934/cpaa.2021031
##### References:

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##### References:
Reference configuration of the two-dimensional example
the deformed configuration at several times
the deformed configuration at $c_1 = c_2 = a = 0.1$ and $c_1 = c_2 = a = 1$
the temperature field at $\theta_R = 0$ and $\theta_R = 8$
the deformed configuration at t = 0.5s and t = 1s
the deformed configuration at $\theta_R = 0$ and $\theta_R = 10$
the deformed configuration at $\theta_R = 0$ and $\theta_R = 8$
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