Application of the Fenchel Theorem to the Obstacle Problem

Abstract : In this paper we apply a duality algorithm to the general obstacle problem for second order operators. We reduce the problem to the null obstacle case and we solve it by using an algorithm based on a dual approximate problem. This method generates a quadratic minimization problem, which is easy to implement numerically. The convergence properties and the numerical results show that the algorithm is working properly for any admissible obstacle.