A Moving Mesh Finite Element Method for the Solution of Two-Dimensional Stefan Problems

An r-adaptive moving mesh method is developed for the numerical solution of an enthalpy formulation of two-dimensional heat conduction problems with a phase change. The grid is obtained from a global mapping of the physical to the computational domain which is designed to cluster mesh points around the interface between the two phases of the material. The enthalpy equation is discretised using a semi-implicit Galerkin finite element method using linear basis functions. The moving finite element method is applied to problems where the phase front is cusp shaped and where the interface changes topology.