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About 80 participants from 16 countries attended the Conference on Numerical Methods for Free Boundary Problems, held at the University of Jyviiskylii, Finland, July 23-27, 1990. The main purpose of this conference was to provide up-to-date information on important directions of research in the field of free boundary problems and their numerical solutions. The contributions contained in this volume cover the lectures given in the conference. The invited lectures were given by H.W. Alt, V. Barbu, K-H. Hoffmann, H. Mittelmann and V. Rivkind. In his lecture H.W. Alt considered a mathematical model and existence theory for non-isothermal phase separations in binary systems. The lecture of V. Barbu was on the approximate solvability of the inverse one phase Stefan problem. K-H. Hoff mann gave an up-to-date survey of several directions in free boundary problems and listed several applications, but the material of his lecture is not included in this proceedings. H.D. Mittelmann handled the stability of thermo capillary convection in float-zone crystal growth. V. Rivkind considered numerical methods for solving coupled Navier-Stokes and Stefan equations. Besides of those invited lectures mentioned above there were 37 contributed papers presented. We shall briefly outline the topics of the contributed papers: Stefan like problems. Modelling, existence and uniqueness.

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Invited lectures.- A mathematical model and an existence theory for non-isothermal phase separation.- The approximate solvability of the inverse one phase Stefan problem.- Stability of Thermocapillary Convection in Float-Zone Crystal Growth.- Numerical solution of coupled Navier-Stokes and Stefan equations.- Contributed papers.- On approximation of the inverse one-phase Stefan problem.- Front-Tracking and Variational Methods to Approximate Interfaces with Prescribed Mean Curvature.- Mixed elements and a two-phase free-boundary problem in magnetostatics.- Numerical solutions of two phase continuous casting problem.- Numerical analysis of capillary free boundaries governed by the Navier-Stokes equations.- Optimal design for transonic flows.- Penalties and Mixed Finite Element Analysis for Variational Inequalities.- The nonuniqueness in a model for phase transitions in binary alloys.- On the behaviour of mushy region in a Stefan problem.- Optimal control of hemivariational inequalities. Approximation results.- A thermodynamical model of ferromagnetism and its numerical simulation.- Computational stability of an initially radial solution of a growth/dissolution problem in a nonradial implementation.- Shape Optimization for Multi-Phase Stefan Problems.- Semi-analytical investigation of unsteady free-boundary flows.- On the convergence of solutions in problems of optimal control of variational inequality of the fourth-order.- A fixed-grid finite element method for solidification.- Domain decomposition method to realize implicit mesh schemes for some singular parabolic equations.- A mathematical model of a two-phase region in thawing soil.- An axisymmetric analysis of thermal effects during cementation of femoral prostheses.- Front Tracking of Free Boundaries with Curvature Terms.- Mixed variational approach for shape optimization in contact problem with prescribed friction.- Nonsmooth Penalty Techniques in Control of the Continuous Casting Process.- Optimal control for state constrained two-phase Stefan problems.- On a free boundary problem of earth dams with separated-variable filtration coefficients.- Design and Efficient Implementation of an Adaptive FEM for Parabolic FBPs.- A Domain Decomposition Technique Applied to a Free Surface Seepage Problem.- Numerical investigation of soliton generation by a moving region of surface pressure.- Eigenfrequencies of a viscous, incompressible fluid with a capillary free boundary.- The Stefan problem for a hyperbolic heat equation.- Numerical method for free-surface hydrodynamical problems.- FDM approximation of variational inequalities with an application to injection moulding.- A linear approach for the nonlinear distributed parameter identification problem.- Long wave approximation for vortex free boundary flows.- Numerical solution of free boundary problem in optimal control of nonlinear systems.- Control problem of nonlinear dynamical systems with phase constraints.

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