This book is devoted to the definition, analysis and implementation of a new numerical algorithm for the approximation of elliptic equations defined on general domains and its application to the problems of Stefan. These problems are used to model the multiphase physical phenomena, such as the melting of ice, dendritic solidification or crystal growth. From the mathematical point of view, the problems of Stefan consist a system of partial differential equations(PDE) governing simultaneously the quantities on an open domain (or a family of open domains) and its boundary (or their boundaries)....