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

Daniel Kessler (1) , Jean-Francois Scheid (2, 3, 4)

1 EPFL - Ecole Polytechnique Fédérale de Lausanne
2 CORIDA - Robust control of infinite dimensional systems and applications
3 UHP - Université Henri Poincaré - Nancy 1
4 IECN - Institut Élie Cartan de Nancy

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.

Mots clés: phase field model; parabolic system; finite element; a priori error estimates

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Daniel Kessler, Jean-Francois Scheid. A priori error estimates of a finite-element method for an isothermal phase-field model related to the solidification process of a binary alloy. IMA Journal of Numerical Analysis, 2002, 22 (2), pp.281-305. ⟨10.1093/imanum/22.2.281⟩. ⟨hal-03116814⟩