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

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Abstract

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.

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  1. Faculty of Mathematics, Chemnitz University of Technology, 09107, Chemnitz, Germany

    Martin K. Bernauer & Roland Herzog

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  1. Martin K. Bernauer
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  2. Roland Herzog
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Correspondence to Martin K. Bernauer.

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Bernauer, M.K., Herzog, R. Implementation of an X-FEM Solver for the Classical Two-Phase Stefan Problem. J Sci Comput 52, 271–293 (2012). https://doi.org/10.1007/s10915-011-9543-x

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