ABSTRACT
In this chapter, we present the moving finite element method (MFEM) with piecewise polynomial approximations of arbitrary degree to solve onedimensional and two-dimensional moving boundary problems or Stefan problems with one or more moving interfaces. For the purpose of increasing the numerical accuracy in the simulation of the important class of Stefan problems, some techniques concerning the treatment of the starting solution when the space domain has an initial zero thickness are developed. The knowledge of the boundary and initial conditions and the pseudo-steady-state solution is applied to find a correct initialization of the numerical model. The techniques investigated are efficient and accurate for solving a large number of problems involving moving boundary interfaces.
