Commun. Comput. Phys., 15 (2014), pp. 506-555.

Phase Field Models Versus Parametric Front Tracking Methods: Are They Accurate and Computationally Efficient?

John W. Barrett 1, Harald Garcke 2*, Robert Nurnberg 1

1 Department of Mathematics, Imperial College London, London, SW7 2AZ, UK.
2 Fakultat fur Mathematik, Universitat Regensburg, 93040 Regensburg, Germany.

Received 19 March 2013; Accepted (in revised version) 1 August 2013
Available online 27 September 2013


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.

AMS subject classifications: 35K55, 35R35, 35R37, 53C44, 65M12, 65M50, 65M60, 74E10, 74E15, 74N20, 80A22, 82C26

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Key words: Phase field models, parametric sharp interface methods, Stefan problem, anisotropy, solidification, crystal growth, numerical simulations, benchmark problems.

*Corresponding author.
Email: (J. W. Barrett), (H. Garcke), (R. Nurnberg)

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