Coupling regularization and adaptive hp-BEM for the solution of a delamination problem

Abstract

In this paper, we couple regularization techniques with the adaptive hp-version of the boundary element method (hp-BEM) for the efficient numerical solution of linear elastic problems with nonmonotone contact boundary conditions. As a model example we treat the delamination of composite structures with a contaminated interface layer. This problem has a weak formulation in terms of a nonsmooth variational inequality. The resulting hemivariational inequality is first regularized and then discretized by an adaptive hp-BEM. We give conditions for the uniqueness of the solution and provide an a-priori error estimate. Furthermore, we prove the very first a-posteriori error estimate for the nonsmooth variational problem utilizing a novel mixed regularized formulation, thus enabling hp-adaptivity. Various numerical experiments illustrate the behavior, strengths and limitations of the proposed high-order approximation scheme.