An iterative domain decomposition method for free boundary problems with nonlinear flux jump constraint

In this paper we design an iterative domain decomposition method for free boundary problems with nonlinear flux jump condition. Our approach is related to damped Newton's methods. The proposed scheme requires, in each iteration, the approximation of the flux on (both sides of) the free interface. We present a Finite Element implementation of our method. The numerical implementation uses harmonically deformed triangulations to inexpensively generate finite element meshes in subdomains. We apply our method to a simplified model for jet flows in pipes and to a simple magnetohydrodynamics model. Finally, we present numerical examples studying the convergence of our scheme.