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A priori error estimates of a finite‐element method for an isothermal phase‐field model related to the solidification process of a binary alloy

Kessler, D. ; Scheid, J.‐F

In: IMA Journal of Numerical Analysis, 2002, vol. 22, no. 2, p. 281-305

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    Titre
    • A priori error estimates of a finite‐element method for an isothermal phase‐field model related to the solidification process of a binary alloy
    Auteur
    • Kessler, D.. Département de Mathématiques, Ecole Polytechnique Fédérale, 1015 Lausanne, Switzerland
    • Scheid, J.‐F. Université Henri Poincaré Nancy 1, Institut Elie Cartan, B.P. 239, 54506 Vandoeuvre‐les‐Nancy Cédex, France
    Type de document
    • Postprint
    Langue
    • Anglais
    Publié dans
    • IMA Journal of Numerical Analysis, 2002, vol. 22, no. 2, p. 281-305. Oxford University Press
    Autre version électronique
    Identifiant OAI-PMH
    • oai:doc.rero.ch:303640
    Summary
    We introduce a piecewise linear finite‐element scheme with semi‐implicit time discretization for an evolutionary phase field system modelling the isothermal solidification process of a binary alloy. This system can be written in a vectorial form as a nonlinear parabolic system. The convergence of the scheme with error estimate is then proved by introducing a generalized vectorial elliptic projector