The extended finite element method (XFEM) for solidification problems

An enriched )nite element method for the multi-dimensional Stefan problems is presented. In this method the standard )nite element basis is enriched with a discontinuity in the derivative of the temperature normal to the interface. The approximation can then represent the phase interface and the associated discontinuity in the temperature gradient within an element. The phase interface can be evolved without re-meshing or the use of arti)cial heat capacity techniques. The interface is described by a level set function that is updated by a stabilized )nite element scheme. Several examples are solved by the proposed method to demonstrate the accuracy and robustness of the method