Convergence analysis on a numerical algorithms for a class of double obstacle problems

In this paper we propose a new iterative algorithm for the solution of a certain class of double obstacle problems. Such problems arise in the modeling of a variety of physical phenomena and usually involve the determination of an unknown free boundary. Here we describe a way of locating the free boundary directly and provide a proof that the algorithm converges when used with analytic methods. The advantage of this algorithm is that it can be used in conjunction with any numerical method with minimal development of extra code.