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Phase field models versus parametric front tracking methods: are they accurate and computationally efficient? (English) Zbl 1388.65096

Summary: We critically compare the practicality and accuracy of numerical approximations of phase field models and sharp interface models of solidification. Here we focus on Stefan problems, and their quasi-static variants, with applications to crystal growth. New approaches with a high mesh quality for the parametric approximations of the resulting free boundary problems and new stable discretizations of the anisotropic phase field system are taken into account in a comparison involving benchmark problems based on exact solutions of the free boundary problem.

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35K55 Nonlinear parabolic equations
80A22 Stefan problems, phase changes, etc.
82C26 Dynamic and nonequilibrium phase transitions (general) in statistical mechanics
82C80 Numerical methods of time-dependent statistical mechanics (MSC2010)
82D25 Statistical mechanics of crystals
35R35 Free boundary problems for PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
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