Boundary element methods for variational inequalities

In this paper we present a priori error estimates for the Galerkin solution of variational inequalities which are formulated in fractional Sobolev trace spaces, i.e. in H˜1/2(Γ). In addition to error estimates in the energy norm we also provide, by applying the Aubin–Nitsche trick for variational inequalities, error estimates in lower order Sobolev spaces including L2(Γ). The resulting discrete variational inequality is solved by using a semi-smooth Newton method, which is equivalent to an active set strategy. A numerical example is given which confirms the theoretical results.