Regularization method and <i>a posteriori</i> error estimates for the two membranes problem

Abstract

Abstract This study presents a regularization method for the two membranes problem with non-homogeneous boundary conditions. We establish both convergence results and a priori estimates for this method. Using duality theory from convex analysis, we identify the dual problem related to the two membranes problem. Based on this dual formulation, we give a posteriori error estimates for both the continuous and discrete versions of the problem. These a posteriori error estimates are crucial for the practical implementation of the regularized problem.