Comptes Rendus
Ordinary differential equations/Numerical analysis
Numerical analysis of an isotropic phase-field model with magnetic-field effect
Comptes Rendus. Mathématique, Volume 353 (2015) no. 3, pp. 219-224.

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.

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.

Published online:
DOI: 10.1016/j.crma.2014.12.002

Amer Rasheed 1; Abdul Wahab 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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     title = {Numerical analysis of an isotropic phase-field model with magnetic-field effect},
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Amer Rasheed; Abdul Wahab. Numerical analysis of an isotropic phase-field model with magnetic-field effect. Comptes Rendus. Mathématique, Volume 353 (2015) no. 3, pp. 219-224. doi : 10.1016/j.crma.2014.12.002.

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