Free surfaces: Shape sensitivity analysis and numerical methods

In this paper we consider numerical methods for stationary free boundary pr oblems. We start by analysing systematically different shape optimization f ormulations of a model problem and show how the optimality conditions relat e 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 implementat ion for a model problem together with numerical tests is presented. Copyrig ht (C) 1999 John Wiley & Sons, Ltd.