Ordinary differential equations/Numerical analysis
Numerical analysis of an isotropic phase-field model with magnetic-field effect
[Analyse numérique d'un modéle isotrope de champ de phase sous l'effet d'un champ magnétique]

Présenté par : Philippe G. Ciarlet

Rasheed, Amer1 ; Wahab, Abdul2
1 Department of Mathematics, School of Science and Engineering, Lahore University of Management Sciences, Opposite Sector U, DHA, Lahore Cantt 54792, Pakistan
2 Department of Mathematics, COMSATS Institute of Information Technology, G.T. Road, 47040, Wah Cantt., Pakistan
Comptes Rendus. Mathématique, Tome 353 (2015) no. 3, pp. 219-224.

Le but de cette note est d'effectuer l'analyse numérique d'un modèle isotrope de champ de phase pour la solidification dendritique d'un alliage binaire sous l'effet d'un champ magnétique appliqué dans un environnement isotherme. Précisément, la stabilité numérique et l'analyse d'erreur du schéma d'approximation éléments finis sont effectuées. L'exemple particulier d'un alliage binaire nickel–cuivre (Ni–Cu) est considéré. L'étude montre un bon accord entre les résultats numériques et théoriques.

The aim of this letter is to perform the numerical analysis of an isotropic phase-field model for dendritic solidification of a binary alloy subject to an applied magnetic field in an isothermal environment. Precisely, the numerical stability and error analysis of a finite-element-based approximation scheme are performed. The particular example of a nickel–copper (Ni–Cu) binary alloy is considered. The study substantiates a good agreement between the numerical and theoretical results.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2014.12.002
Rasheed, Amer 1 ; Wahab, Abdul 2

1 Department of Mathematics, School of Science and Engineering, Lahore University of Management Sciences, Opposite Sector U, DHA, Lahore Cantt 54792, Pakistan
2 Department of Mathematics, COMSATS Institute of Information Technology, G.T. Road, 47040, Wah Cantt., Pakistan 
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Rasheed, Amer; Wahab, Abdul. Numerical analysis of an isotropic phase-field model with magnetic-field effect. Comptes Rendus. Mathématique, Tome 353 (2015) no. 3, pp. 219-224. doi : 10.1016/j.crma.2014.12.002. http://www.numdam.org/articles/10.1016/j.crma.2014.12.002/

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