Stabilization techniques and a posteriori error estimates for the obstacle problem

This work deals with a posteriori error estimates for the obstacle problem. Deriving an estimator on the basis of the variational inequality with respect to the primal variable, an inconsistent one is obtained. To achieve consistency, this problem is treated by a Lagrange formalism, which transfers the variational inequality into a saddle point problem. Different techniques to ensure the stability of the discretization and to solve the discrete problems by iterative solvers are studied and compared. Numerical tests confirm our results of consistent a posteriori error estimation.