An inverse finite element method for directly formulated free boundary problems

In free boundary problems, in addition to the primary field variables, velocity, pressure and temperature, unknown geometric parameters need to be evaluated. A characteristic feature of the problems is a demarcation line which separates two domains with different material properties. The problems are highly non-linear and difficult to handle computationally. Here an accurate and efficient method is presented which can appropriately handle the complexities associated with these problems. The method is based on a tesselation that is constructed by isolines as characteristic co-ordinate lines. Thus opposite sides of finite elements lie on isolines. The method allows the simultaneous determination of the location of the isolines with the primary unknowns. Its accuracy and efficiency is demonstrated in a number of one and two dimensional steady and unsteady model problems.