Trace and flux a priori error estimates in finite element approximations   of Signorni-type problems
  Variational inequalities play in many applications an important role and are an active research area. Optimal a priori error estimates in the natural energy norm do exist but only very few results in other norms exist. Here we consider as prototype a simple Signorini problem and provide new optimal order a priori error estimates for the trace and the flux on the Signorini boundary. The a priori analysis is based on the exact and a mesh-dependent Steklov-Poincar\'e operator as well as on duality in Aubin-Nitsche type arguments. Numerical results illustrate the convergence rates of the finite element approach. 
Olaf Steinbach, Barbara Wohlmuth, Linus Wunderlich
math.NA