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The extended finite element method (XFEM) for solidification problems. (English) Zbl 1003.80004
Summary: An enriched finite element method for the multi-dimensional Stefan problems is presented. In this method the standard finite 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 artificial heat capacity techniques. The interface is described by a level set function that is updated by a stabilized finite element scheme. Several examples are solved by the proposed method to demonstrate the accuracy and robustness of the method.

MSC:
80M10 Finite element, Galerkin and related methods applied to problems in thermodynamics and heat transfer
80A22 Stefan problems, phase changes, etc.
Software:
XFEM
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