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Finite element approximation of a model for phase separation of a multi-component alloy with non-smooth free energy. (English) Zbl 0882.65129
This is a long and yet compactly written paper with many nice features. The authors consider a partial differential equation model for the isothermal phase separation of a multicomponent mixture, when quenched into an unstable state. A piecewise linear finite element approximation is used and combined with a backward Euler time discretization; the resulting nonlinear equations are solved iteratively. The authors analyze the computations and provide error bounds. Numerical experiments are performed in one and two space dimensions. In the one-dimensional case some computed steady states are compared with explicitly constructed solutions to the stationary equations.
Reviewer: W.Govaerts (Gent)

MSC:
65Z05 Applications to the sciences
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35Q72 Other PDE from mechanics (MSC2000)
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
80A22 Stefan problems, phase changes, etc.
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