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Stability and convergence of two discrete schemes for a degenerate solutal non-isothermal phase-field model. (English) Zbl 1171.80006
The mathematical model studied in this work describes the solidification process occurring in a binary alloy with temperature-dependent properties. It is based on a highly non-linear parabolic system of partial differential equations with three dependent variables: phase-field, solute concentration and temperature. The authors analyze two numerical schemes of Euler type in time and \(C^0\) finite-element type with \(\mathbb{P}_1\)-approximation in space for solving a phase-field model of the problem. The first scheme is nonlinear, unconditionally stable and convergent. Whereas the second scheme is linear but conditionally stable and convergent.

80M10 Finite element, Galerkin and related methods applied to problems in thermodynamics and heat transfer
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
80A22 Stefan problems, phase changes, etc.
35K65 Degenerate parabolic equations
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
Full Text: DOI EuDML
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