Regularization method and a posteriori error estimates for the bilateral obstacle problem

In this paper, we present a relatively complete analysis of the regularization method for of the bilateral obstacle problem with a non-homogeneous condition on the boundary. We provide both the convergence result and a priori estimates. Then by the duality theory from the convex analysis, we determine the dual problem associated with the of the bilateral obstacle problem. Based on this dual problem, we provide a posteriori error estimates for the continuous and the discrete problems. The a posteriori error estimates are desired for the practical implementation of the regularized problem.