General approach for a posteriori error estimates for finite element solutions of variational inequalities

  A general approach for a posteriori error estimates for finite element solutions of variational inequalities is proposed. The ideas are based on the experiences in Blum and Suttmeier [3, 4]. The bounds for controlling arbitrary functionals of the discretisation error are constructed by using a duality argument, similar to the concept proposed, e.g., in Becker and Rannacher [2] for variational equalities. The application of the abstract framework is illustrated at a plasticity, the obstacle and Signorini's problem.