Barrett, John W.; Garcke, Harald; Nürnberg, Robert Phase field models versus parametric front tracking methods: are they accurate and computationally efficient? (English) Zbl 1388.65096 Commun. Comput. Phys. 15, No. 2, 506-555 (2014). 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. Cited in 2 Documents 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 PDFBibTeX XMLCite \textit{J. W. Barrett} et al., Commun. Comput. Phys. 15, No. 2, 506--555 (2014; Zbl 1388.65096) Full Text: DOI arXiv