Work

A discrete scheme for regularized anisotropic surface diffusion: a 6th order geometric evolution equation

Year: 2005

Type: article

Abstract: 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.

Source: Interfaces and Free Boundaries Mathematical Analysis Computation and Applications

DOI: 10.4171/ifb/129

Authors: Frank Hausser, Christian Voigt

Institutions: Center of Advanced European Studies and Research, University of Glasgow

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funder: Bundesministerium für Bildung und Forschung

OpenAlex ID: W2069448348

FWCI: 4.632

Cites: 25

Cited by: 29

Related to: 10