Analysis of an elastic-rigid obstacle problem described by a variational-hemivariational inequality

In this paper, we consider a new obstacle problem for the elastic membrane lying above an elastic-rigid obstacle. The elastic-rigid obstacle allows limited penetration and offers a nonmonotone reactive force. We introduce the mathematical model and prove that its weak form, which is a variational-hemivariational inequality, has a unique solution. Then, we consider a discrete scheme to solve the problem. The optimal-order error estimate under appropriate regularity assumptions is derived. Finally, numerical examples are reported, from which the theoretical predicted optimal-order error estimate can be clearly observed.