A priori error estimate of virtual element method for a quasivariational–hemivariational inequality

Abstract

In this paper, the virtual element method is used to solve a frictional contact problem which can be characterized by an elliptic quasivariational–hemivariational inequality. After reviewing the existence and uniqueness of the solution, we present the construction of virtual element spaces and corresponding numerical scheme. Furthermore, a Céa’s inequality for error estimation is established, and an optimal order error bound is derived under appropriate solution regularity assumptions. Numerical results are presented to illustrate the theoretical prediction of the convergence order.