The adaptive mesh design based on an a posteriori error control is studied for the finite element discretizations of variational problems of Signorini type. The authors extend the techniques to derive residual based error estimators to variational inequalities employing a suitable adaptation of the duality argument. By use of this variational argument weighted a posteriori estimates for controlling arbitrary functionals of the error are derived (for model situations for contact problems).
Main result: All arguments are based on Hilbert space methods and can be carried over to the more general situation of linear elasticity. Numerical examples demonstrated that the approach leads to effective strategies for designing economical meshes and to bounds for the error which are useful in practice.