Zentrum für Technomathematik Fachbereich 3 – Mathematik und Informatik Solving the Stefan problem with prescribed interface using an XFEM toolbox for FENICS

In this article, we consider the Stefan problem with prescribed interface as an example for a process with a time-dependent discontinuity. While there are various methods for solving these type of problems, the extended finite element method has grown popularity due to its flexibility. Partly based on the work of Nikbakht et al., we developed an XFEM toolbox within the FEniCS framework to solve time-dependent problems with arbitrary discontinuities. This toolbox is tested by considering different model variants of the Stefan problem. Numerical results and convergence analysis are presented which show the success of the chosen approach.