The Virtual Element Method for an Elliptic Hemivariational Inequality with Convex Constraint

Abstract

An abstract framework of numerical method is devised for solving an elliptic hemivariational inequality with convex constraint. Convergence of the method is explored under the minimal solution regularity available from the well-posedness of the hemivariational inequality. A Céa-type inequality is derived for error estimation. As a typical example, a virtual element method is proposed to solve a frictionless unilateral contact problem and its optimal error estimates are obtained as well. Numerical results are reported to show the performance of the proposed method.