A direct algorithm in some free boundary problems

In this paper we propose a new algorithm for the well known elliptic obstacle problem and for parabolic variational inequalities like oneand two-phase Stefan problem and of obstacle type. Our approach enters the category of xed domain methods and solves just linear elliptic or parabolic equations and their discretization at each iteration. We prove stability and convergence properties. The approximating coincidence set is explicitly computed and it converges in the Hausdor –Pompeiu sense to the searched geometry. In the numerical examples, the algorithm has a very fast convergence and the obtained solutions (including the free boundaries) are accurate.