Adaptive hp-versions of BEM for Signorini problems Original Research Article

In this paper we analyze the hp-discretization of a boundary integral formulation for the Signorini contact problem of the Laplacian. We prove convergence of the bem Galerkin solution in the energy norm and obtain, under mild regularity assumptions, an a priori error estimate. Using a hierarchical subspace decomposition we derive a reliable and efficient a posteriori error estimate. Based on the hierarchical estimators we present a three-step hp-adaptive algorithm and present numerical results which yield appropriate mesh refinements and polynomial degree distributions.