# The constrained natural element method (C-NEM) for treating thermal models involving moving interfaces

Abstract : In this paper, the features of the natural neighbor (Sibson) interpolant are used within the context of a constrained Voronoi diagram, dual to the constrained Delaunay triangulation, for treating moving interface (Stefan) problems. The constrained natural element method (C-NEM) uses the Voronoi cells instead of the Delaunay triangles for both interpolation and integration, and thus permits the use of very distorted triangles in the Delaunay triangulation without loss of accuracy. The resulting interpolation is $C^1$ ($C^\infty$ in the most part of the domain) everywhere except at the nodes and across the interface, where it is $C^0$, which allows an accurate treatment of models involving moving interfaces. Numerical experiments are performed for proving the accuracy of the method, as well as its promise.
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https://hal.archives-ouvertes.fr/hal-01508705
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Julien Yvonnet, Francisco Chinesta, Philippe Lorong, David Ryckelynck. The constrained natural element method (C-NEM) for treating thermal models involving moving interfaces. International Journal of Thermal Sciences, Elsevier, 2005, 44 (6), pp.559 - 569. ⟨10.1016/j.ijthermalsci.2004.12.007⟩. ⟨hal-01508705⟩

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