Analysis and numerical study of a mixed formulation of a two membranes problem

In this paper, we present a reformulation of a two membranes problem as a mixed formulation problem based on the subdifferential of a continuous function of which the subdifferential leads to the characterization of the coincidence set. The reformulated problem is transformed into a saddle point problem. Then we present an iterative method to solve the problem and we prove the convergence of the approximate solutions to the exact one. Finally, some numerical examples are given.