Numerical solution of an adhesion problem with FEM and BEM

This paper treats a class of linear-elastic problems with nonlinear nonsmooth boundary conditions. Solutions can be found by the minimization of an associated potential function. While the finite element method is usually employed for discrete approximations, the existing framework of hemivariational inequalities can also be applied to boundary element formulations. Conditions for the strict convexity of the associated potential function are given, together with a more general criterion for the uniqueness of a solution. Finally, some numerical benchmarks in 2D and 3D are given. A residual error estimator is suggested and successfully applied to the FE computations.