Time discretizations of anisotropic Allen-Cahn equations
Gräser C, Kornhuber R, Sack U (2013)
Publication Type: Journal article
Publication year: 2013
Journal
Book Volume: 33
Pages Range: 1226-1244
Journal Issue: 4
Abstract
We consider anisotropic Allen-Cahn equations with interfacial energy induced by an anisotropic surface energy density γ. Assuming that γ is positive, positively homogeneous of degree 1, strictly convex in tangential directions to the unit sphere and sufficiently smooth, we show the stability of various time discretizations. In particular, we consider a fully implicit and a linearized time discretization of the interfacial energy combined with implicit and semiimplicit time discretizations of the double-well potential. In the semiimplicit variant, concave terms are taken explicitly. The arising discrete spatial problems are solved by globally convergent truncated nonsmooth Newton multigrid methods. Numerical experiments show the accuracy of the different discretizations. We also illustrate that pinch-off under anisotropic mean curvature flow is no longer invariant under rotation of the initial configuration for a fixed orientation of the anisotropy. © The authors 2013. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
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Germany (DE)How to cite
APA:
Gräser, C., Kornhuber, R., & Sack, U. (2013). Time discretizations of anisotropic Allen-Cahn equations. IMA Journal of Numerical Analysis, 33(4), 1226-1244. https://doi.org/10.1093/imanum/drs043
MLA:
Gräser, Carsten, Ralf Kornhuber, and Uli Sack. "Time discretizations of anisotropic Allen-Cahn equations." IMA Journal of Numerical Analysis 33.4 (2013): 1226-1244.
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