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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 257104, 6 pages
Research Article

Theoretical Framework of a Variational Formulation for Nonlinear Heat Transfer with Phase Changes

1Université de Lyon, ENISE, LTDS, UMR 5513 CNRS, 58 rue Jean Parot, 42023 Saint-Etienne Cedex 2, France
2Université de Lyon, ENISE, DIPI, EA 3719, 58 rue Jean Parot, 42023 Saint-Etienne Cedex 2, France

Received 28 September 2012; Revised 20 November 2012; Accepted 21 November 2012

Academic Editor: Diego J. Celentano

Copyright © 2013 Eric Feulvarch et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper discusses mathematical results for a variational formulation dedicated to heat transfer with phase changes. Practical finite element experiences show that the studied formulation can lead to difficulties for the numerical resolution at each time step. The aim of the paper is to show that such numerical pathologies do not come from the basic variational formulation by showing existence and uniqueness of the solution.