Virtual element method for a frictional contact problem with normal compliance

We consider an elastostatic frictional contact problem with a normal compliance condition and Coulomb’s law of dry friction, which can be modeled by a quasi-variational inequality. As a generalization of the finite element method, the virtual element method (VEM) can handle general polygonal meshes with hanging nodes, which are very suitable for solving problems with complex geometries or applying adaptive mesh refinement strategy. In this paper, we study the VEM for solving the frictional contact problem with the normal compliance condition. Existence and uniqueness results are obtained for the discretized scheme. Furthermore, a priori error analysis is established, and an optimal order error bound is derived for the lowest order virtual element method. One numerical example is given to show the efficiency of the method and to illustrate the theoretical error estimate. • The virtual element method is studied for solving a quasi-variational inequality. • Existence and uniqueness are proved for the discretized scheme. • An optimal error estimate is derived for the lowest-order virtual element scheme.