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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. (English) Zbl 1001.76057
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 binary alloy. This system can be written in vectorial forin as a nonlinear parabolic system. The convergence of the scheme with error estimate is then proved by introducing a generalized vectorial elliptic projector.

MSC:
76M10 Finite element methods applied to problems in fluid mechanics
76T99 Multiphase and multicomponent flows
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
80A22 Stefan problems, phase changes, etc.
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