Analysis of a contact problem with unilateral constraint and slip-dependent friction

We consider a mathematical model which describes the equilibrium of an elastic body in frictional contact with an obstacle. The contact is modelled with normal compliance and unilateral constraint, associated with a slip-dependent version of Coulomb's law of dry friction. We present a weak formulation of the problem, then we state and prove an existence and uniqueness result of the solution. The proof is based on arguments of elliptic quasivariational inequalities. We also study the finite element approximations of the problem and derive error estimates. Finally, we provide numerical simulations which illustrate both the behaviour of the solution related to the frictional contact conditions and the convergence order of the error estimates.