An adaptive finite element discretisation for a simplified Signorini problem

Adaptive mesh design based on a posteriori error control is studied for finite element discretisations for variational problems of Signorini type. The techniques to derive residual based error estimators developed, e.g., in ([2,10,20]) are extended to variational inequalities employing a suitable adaptation of the duality argument [17]. By use of this variational argument weighted a posteriori estimates for controlling arbitrary functionals of the error are derived here for model situations for contact problems. All arguments are based on Hilbert space methods and can be carried over to the more general situation of linear elasticity. Numerical examples demonstrate that this approach leads to effective strategies for designing economical meshes and to bounds for the error which are useful in practice.