91 citations · 747 across the 46 of their papers we have counts for
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Phase Field Models versus Parametric Front Tracking Methods: Are they accurate and computationally efficient?
John W. Barrett, Harald Garcke, Robert Nürnberg
We critically compare the practicality and accuracy of numerical approximations of phase field models and sharp interface models of solidification. Particular emphasis is put on St…
Stable Phase Field Approximations of Anisotropic Solidification
John W. Barrett, Harald Garcke, Robert Nürnberg
We introduce unconditionally stable finite element approximations for a phase field model for solidification, which take highly anisotropic surface energy and kinetic effects into…
On the stable discretization of strongly anisotropic phase field models with applications to crystal growth
John W. Barrett, Harald Garcke, Robert Nürnberg
We introduce unconditionally stable finite element approximations for anisotropic Allen--Cahn and Cahn--Hilliard equations. These equations frequently feature in phase field models…
Numerical computations of facetted pattern formation in snow crystal growth
John W. Barrett, Harald Garcke, Robert Nürnberg
Facetted growth of snow crystals leads to a rich diversity of forms, and exhibits a remarkable sixfold symmetry. Snow crystal structures result from diffusion limited crystal growt…
Finite-Element Approximation of One-Sided Stefan Problems with Anisotropic, Approximately Crystalline, Gibbs--Thomson Law
John W. Barrett, Harald Garcke, Robert Nürnberg
We present a finite-element approximation for the one-sided Stefan problem and the one-sided Mullins--Sekerka problem, respectively. The problems feature a fully anisotropic Gibbs-…