# Boundary element methods for variational inequalities

## Univ.-Prof. Dr. Olaf Steinbach

June 15, 2012, 9 a.m. S2 416

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.