188 citations · 1.6k across the 107 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 an Incompressible Navier-Stokes/Cahn-Hilliard System with Degenerate Mobility
Helmut Abels, Daniel Depner, Harald Garcke
We prove existence of weak solutions for a diffuse interface model for the flow of two viscous incompressible Newtonian fluids in a bounded domain by allowing for a degenerate mobi…
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…
Mean curvature flow with triple junctions in higher space dimensions
Daniel Depner, Harald Garcke, Yoshihito Kohsaka
We consider mean curvature flow of n-dimensional surface clusters. At (n-1)-dimensional triple junctions an angle condition is required which in the symmetric case reduces to the w…
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…