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A Time Fractional Hemivariational Inequality Arising from a Dynamic Contact Problem: Analysis and Numerical Simulation
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DOI：10.1007/s10915-026-03418-1.png)
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Abstract
En 中文
This paper investigates a dynamic frictional contact problem for a viscoelastic body interacting with a foundation. The constitutive law, equation of motion, and boundary conditions all involve time-fractional derivatives. The normal compliance condition and friction law are modeled via Clarke subdifferentials, leading to a time-fractional hemivariational inequality. We reformulate it as an equivalent problem incorporating both fractional derivatives and integrals. By applying the Banach fixed-point theorem alongside existing results for hemivariational inequalities, we establish the existence of a unique weak solution. Furthermore, a priori error estimates are derived for semi-discrete and fully-discrete numerical schemes. Numerical simulations are presented to verify the theoretical conclusions.
Keywords:
Hemivariational inequality
Dynamic contact problem
Finite element method
Error estimates
Time fractional derivative
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3.3
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652
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