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<p>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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年2月12日

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  • Hailing Xuan,
  • Xiaoliang Cheng,
  • Lele Yuan

摘要

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.