Journal of Scientific Computing

, Volume 52, Issue 2, pp 271–293 | Cite as

Implementation of an X-FEM Solver for the Classical Two-Phase Stefan Problem

  • Martin K. Bernauer
  • Roland Herzog


The classical two-phase Stefan problem in level set formulation is considered. The implementation of a solver on triangular grids is described. Extended finite elements (X-FEM) in space and an implicit Euler method in time are used to approximate the temperature. For the level set equation, a discontinuous Galerkin (DG) and a strong stability preserving (SSP) Runge-Kutta scheme are employed. Polynomial spaces of quadratic order are used. A numerical example with a change of topology is provided, and the order of convergence is studied on the Frank sphere example.


Two-phase Stefan problem Solidification Moving boundary problem Level set method Discontinuous Galerkin approximation Extended finite element method 


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Faculty of MathematicsChemnitz University of TechnologyChemnitzGermany

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