Analysis and Numerical Approximation of an Elastic Frictional Contact Problem with Normal Compliance

In this paper we consider a problem of frictional contact between an elastic body and an obstacle. The elastic constitutive law is assumed to be nonlinear. The contact is modeled with normal compliance and the associated version of Coulomb's law of dry friction. We present two alternative yet equivalent weak formulations of the problem, and establish existence and uniqueness results for both formulations using arguments of elliptic variational inequalities and xed point. Moreover, we show the continuous dependence property of the solution with respect to the contact conditions. We also study the nite element approximations of the problem and derive error estimates. Finally, we introduce an iterative method to solve the resulting nite element system.