Kevin T. Andrews, L. Chapman, J. R. Fern\'andez, M. Fisackerly,
M. Shillor, L. Vanerianand T. VanHouten

A model for the process of quasistatic evolution of an elastic membrane in
adhesive contact with a rigid obstacle is developed, analyzed and numerically
simulated. The model consists of an elliptic variational inequality for the membrane
displacements and a nonlinear ordinary differential equation for the evolution of
the adhesion field. By using regularity results from the theory of elliptic variational
inequalities and a fixed point argument the system is shown to have a unique weak
solution. A fully discrete algorithm is described, is shown to converge and its error
estimates are derived. In this process we make critical use of the regularity properties
of the solution. Finally, the results of numerical simulations, based on the fully discrete
algorithm, are presented.