Free surfaces: shape sensitivity analysis and numerical methods

In this paper we consider numerical methods for stationary free boundary problems. We start by analysing systematically di erent shape optimization formulations of a model problem and show how the optimality conditions relate to construction of trial type methods. Shape sensitivity analysis of the free boundary leads also to the so-called total linearization method which combines the good properties of Newton method and trial methods, i.e. fast convergence and relative simplicity of implementation. Detailed implementation for a model problem together with numerical tests is presented. Copyright