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Linked References

1. E. Feulvarch, J. M. Bergheau, and J. B. Leblond, “An implicit finite element algorithm for the simulation of diffusion with phase changes in solids,” International Journal for Numerical Methods in Engineering, vol. 78, no. 12, pp. 1492–1512, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
2. G. Comini, S. Del Guidice, R. W. Lewis, and O. C. Zienkiewicz, “Finite element solution of nonlinear heat conduction problems with special reference to phase change,” International Journal for Numerical Methods in Engineering, vol. 8, no. 3, pp. 613–624, 1974. View at Scopus
3. K. Morgan, R. W. Lewis, and O. C. Zienkiewicz, “An improved algorithm for heat conduction problems with phase change,” vol. 12, no. 7, pp. 1191–1195, 1978. View at Scopus
4. R. W. Lewis and P. M. Roberts, “Finite element simulation of solidification problems,” Applied Scientific Research, vol. 44, no. 1-2, pp. 61–92, 1987. View at Publisher · View at Google Scholar · View at Scopus
5. H. Çetinel, M. Toparli, and L. Özsoyeller, “Finite element based prediction of the microstructural evolution of steels subjected to the Tempcore process,” Mechanics of Materials, vol. 32, no. 6, pp. 339–347, 2000. View at Publisher · View at Google Scholar · View at Scopus
6. W. D. Rolph and K. J. Bathe, “An efficient algorithm for analysis of nonlinear heat transfer with phase changes,” International Journal for Numerical Methods in Engineering, vol. 18, no. 1, pp. 119–134, 1982. View at Scopus
7. Q. T. Pham, “A fast, unconditionally stable finite-difference scheme for heat conduction with phase change,” International Journal of Heat and Mass Transfer, vol. 28, no. 11, pp. 2079–2084, 1985. View at Scopus
8. Q. T. Pham, “Comparison of general-purpose finite-element methods for the Stefan problem,” Numerical Heat Transfer B, vol. 27, no. 4, pp. 417–435, 1995. View at Scopus
9. D. Hömberg, “A numerical simulation of the Jominy end-quench test,” Acta Materialia, vol. 44, no. 11, pp. 4375–4385, 1996. View at Publisher · View at Google Scholar · View at Scopus
10. Y. V. L. N. Murthy, G. Venkata Rao, and P. K. Iyer, “Numerical simulation of welding and quenching processes using transient thermal and thermo-elasto-plastic formulations,” Computers and Structures, vol. 60, no. 1, pp. 131–154, 1996. View at Publisher · View at Google Scholar · View at Scopus
11. H. N. Han, J. K. Lee, H. J. Kim, and Y. S. Jin, “A model for deformation, temperature and phase transformation behavior of steels on run-out table in hot strip mill,” Journal of Materials Processing Technology, vol. 128, no. 1-3, pp. 216–225, 2002. View at Publisher · View at Google Scholar · View at Scopus
12. S. Serajzadeh, “Modelling of temperature history and phase transformations during cooling of steel,” Journal of Materials Processing Technology, vol. 146, no. 3, pp. 311–317, 2004. View at Publisher · View at Google Scholar · View at Scopus
13. V. R. Voller, “An overview of numerical methods for phase change problems,” Advances in Numerical Heat Transfer, vol. 1, pp. 341–375, 1996.
14. V. D. Fachinotti, A. Cardona, and A. E. Huespe, “A fast convergent and accurate temperature model for phase-change heat conduction,” International Journal for Numerical Methods in Engineering, vol. 44, no. 12, pp. 1863–1884, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
15. A. J. Dalhuijsen and A. Segal, “Comparison of finite element techniques for solidification problems,” International Journal for Numerical Methods in Engineering, vol. 23, no. 10, pp. 1807–1829, 1986. View at Scopus
16. M. Rappaz, “Modelling of microstructure formation in solidification processes,” International Materials Reviews, vol. 34, no. 3, pp. 93–123, 1989. View at Scopus
17. N. R. Eyres, D. R. Hartree, J. Ingham, R. Jackson, R. J. Sarjant, and J. B. Wagstaff, “The calculation of variable heat flow in solids,” Philosophical Transactions of the Royal Society of London A, vol. 240, pp. 1–57, 1946. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
18. M. J. Mundim and M. Fortes, “Evaluation of finite element method utilised in the solution of solid-liquid phase change problems,” in Numerical Methods in Thermal Problems, W. Lewis and K. Morgan, Eds., vol. 6, pp. 90–100, Pineridge Press, Swansea, UK, 1989.
19. J. J. Droux, “Three-dimensional numerical simulation of solidification by an improved explicit scheme,” Computer Methods in Applied Mechanics and Engineering, vol. 85, no. 1, pp. 57–74, 1991. View at Scopus
20. P. A. Gremaud, Analyse numerique de problemes de changements de phase lies a des phenomenes de solidification [Ph.D. thesis], Ecole Polytechnique Federale de Lausanne, Lausanne, Switzerland, 1991.
21. B. Nedjar, “An enthalpy-based finite element method for nonlinear heat problems involving phase change,” Computers and Structures, vol. 80, no. 1, pp. 9–21, 2002. View at Publisher · View at Google Scholar · View at Scopus
22. E. Feulvarch and J. M. Bergheau, “An implicit fixed-grid method for the finite-element analysis of heat transfer involving phase changes,” Numerical Heat Transfer B, vol. 51, no. 6, pp. 585–610, 2007. View at Publisher · View at Google Scholar · View at Scopus
23. J.-B. Leblond, “Mathematical results for a model of diffusion and precipitation of chemical elements in solid matrices,” Nonlinear Analysis, vol. 6, no. 2, pp. 297–322, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
24. J.-M. Bergheau and R. Fortunier, Finite Element Simulation of Heat Transfer, ISTE-Wiley, 2010. View at Publisher · View at Google Scholar
25. K.-J. Bathe, Finite Element Procedures, Prentice-Hall, 1996.
26. G. Allaire, Numerical Analysis and Optimization, Oxford University Press, Oxford, UK, 2007.
27. J. Nečas, “Sur une méthode pour résoudre les équations aux dérivées partielles du type elliptique, voisine de la variationnelle,” Annali della Scuola Normale Superiore di Pisa, vol. 16, pp. 305–326, 1962. View at Zentralblatt MATH
28. A. Ern and J.-L. Guermond, Éléments Finis: Théorie, Applications, Mise en œuvre, vol. 36, Springer, Berlin, Germany, 2002.
29. H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Universitext, Springer, New York, NY, USA, 2011.
30. K. Yosida, Functional Analysis, Springer, Berlin, Germany, 1980.