Trace and flux a priori error estimates in finite element approximations of Signorini-type problems

Variational inequalities play an important role in many applications and are an active research area. Optimal a priori error estimates in the natural energy norm do exist, but only very few results are known for different norms. 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 a continuous and a discrete Steklov–Poincaré operator, as well as on Aubin–Nitsche-type duality arguments. Numerical results illustrate the convergence rates of the finite-element approach.