Boundary element methods for variational inequalities

Boundary element methods for variational inequalities

In this talk we present a priori error estimates for the Galerkin solution of variational inequalities which are formulated in fractional Sobolev spaces, i.e. in $\widetilde{H}^{1/2}(\Gamma)$. In addition to error estimates in the energy norm we also provide an error estimate in $L_2(\Gamma)$, by applying the Aubin-Nitsche trick for variational inequalities. 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. Other applications involve boundary value problems with Signorini boundary conditions, and optimal Dirichlet boundary control problems.