The document discusses the simulation of the 1-dimensional Stefan problem using the extended finite element method (XFEM). It provides an overview of the Stefan problem, analytical solution, conventional numerical modeling techniques, and issues with those techniques. It then describes the implementation of XFEM to model the Stefan problem, including enrichment functions, determining enriched degrees of freedom, validation against analytical solutions, and issues encountered, such as determining initial values when the interface is located at a node. Potential extensions to 2D modeling and future work are also discussed.