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Zbl 1183.74272
Feulvarch, E.; Bergheau, J.M.; Leblond, J.B.
An implicit finite element algorithm for the simulation of diffusion with phase changes in solids. (English)
[J] Int. J. Numer. Methods Eng. 78, No. 12, 1492-1512 (2009). ISSN 0029-5981

Summary: A fixed grid technique is proposed for the numerical simulation of the phenomena of diffusion with phase changes in solids. This technique is based on the finite element method in space coupled with the implicit (backward) Euler algorithm in time. The examples given include the Stefan problem, heat transfer with non-instantaneous metallurgical transformations in steels, and the simultaneous and coupled diffusion and precipitation of chemical elements during internal oxidation of steels. These examples clearly evidence the efficiency and robustness of the method developed.

MSC 2000:: *74S05 Finite element methods
74N25 Transformations involving diffusion

Keywords: diffusion; phase changes; finite element method; implicit time integration; Stefan problem; heat transfer; metallurgical transformations; internal oxidation

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Zentralblatt MATH Berlin [Germany]