The virtual element method for general variational–hemivariational inequalities with applications to contact mechanics

Abstract

This paper mainly analyzes the general elliptic variational–hemivariational inequalities with or without constraints by using the virtual element method. The approximations can be internal or external and a Céa’s type inequality is derived for a priori error estimates. Then, we apply the results to a variational–hemivariational inequality arising in frictional contact problems, and the optimal order error estimate is obtained for the linear virtual element solution under appropriate solution regularity assumptions. Finally, numerical simulation results are reported to show the performance of the proposed method, in particular, numerical convergence orders are in good agreement with the theoretical predictions.