Geodesic
A discrete scheme for regularized anisotropic surface diffusion: a 6th order geometric evolution equation
Frank Hausser1 ; Christian Voigt2
1Research Center CAESAR, Bonn, Germany
2University of Glasgow, UK
Interfaces and free boundaries, Tome 7 (2005) no. 4, pp. 353-370

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DOI

We study anisotropic surface diffusion of curves with a small corner energy regularization. The regularization allows the use of non-convex free energy densities and turns the evolution law into a 6th order geometric equation. Using a semi-implicit time discretization, we present a variational formulation of this equation for parametric curves, leading to a discretization based on linear finite elements. The resulting linear system is shown to be uniquely solvable. Numerical examples include the convergence of closed curves to the Wulff shape and the evolution of a thermodynamically unstable surface into a hill-valley structure and its subsequent coarsening.
DOI : 10.4171/ifb/129
Classification : 35-XX, 65-XX, 76-XX, 92-XX
Mots-clés : surface diffusion, anisotropy, 6th order equations, parametric finite elements

Frank Hausser  1   ; Christian Voigt  2

1 Research Center CAESAR, Bonn, Germany
2 University of Glasgow, UK 
Frank Hausser; Christian Voigt. A discrete scheme for regularized anisotropic surface diffusion: a 6th order geometric evolution equation. Interfaces and free boundaries, Tome 7 (2005) no. 4, pp. 353-370. doi: 10.4171/ifb/129
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