Convergences and numerical analysis of a contact problem with normal compliance and unilateral constraint

This paper represents a continuation of a previous study on “Analysis of a Sliding Frictional Contact Problem with Unilateral Constraint”. This study considers a mathematical model which describes the equilibrium of an elastic body in frictional contact with a moving foundation. The contact is modeled with a multivalued normal compliance condition with unilateral constraints, associated to a sliding version of Coulomb’s law of dry friction. After a description of the model, the variational formulation was presented. Then, the dependence of the solution was studied with respect to the data and a convergence result was proven. Regularization method was also used to study the existence and uniqueness of the contact problem for which a convergence result was presented. Finally, a semi-discrete scheme was introduced for the numerical approximation of the sliding contact problem. Under certain solution regularity assumptions, an optimal order error estimate was derived.