Numerical analysis of an evolutionary variational-hemivariational inequality with application in contact mechanics

Variational-hemivariational inequalities are useful in applications in science and engineering. This paper is devoted to numerical analysis for an evolutionary variational-hemivariational inequality. We introduce a fully discrete scheme for the inequality, using a finite element approach for the spatial approximation and a backward finite difference to approximate the time derivative. We present a Céa type inequality which is the starting point for error estimation. Then we apply the results in the numerical solution of a problem arising in contact mechanics, and derive an optimal order error estimate when the linear elements are used. Finally, we report numerical simulation results on solving a model contact problem, and provide numerical evidence on the theoretically predicted optimal order error estimate.