• search hit 6 of 15
Back to Result List

Time discretizations of anisotropic Allen--Cahn equations

Please always quote using this URN:urn:nbn:de:0296-matheon-8885
  • We consider anisotropic Allen--Cahn equations with interfacial energy induced by an anisotropic surface energy density $\gamma$. Assuming that $\gamma$ is positive, positively homogeneous of degree one, strictly convex in tangential directions to the unit sphere, and sufficiently smooth, we show 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 semi-implicit time discretizations of the double-well potential. In the semi-implicit 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 frame invariant, but depends on the orientation of the initial configuration.

Download full text files

Export metadata

Additional Services

Share in Twitter Search Google Scholar
Metadaten
Author:Carsten Gräser, Ralf Kornhuber, Uli Sack
URN:urn:nbn:de:0296-matheon-8885
Referee:Christof Schütte
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2011/08/22
Release Date:2011/08/22
Tag:multigrid; phase transitions; stability; time discretization
Institute:Research Center Matheon
Freie Universität Berlin
Project:C Energy and Materials (Production)
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Mxx Partial differential equations, initial value and time-dependent initial- boundary value problems / 65M12 Stability and convergence of numerical methods
65-XX NUMERICAL ANALYSIS / 65Mxx Partial differential equations, initial value and time-dependent initial- boundary value problems
Preprint Number:816
Verstanden ✔
Diese Webseite verwendet technisch erforderliche Session-Cookies. Durch die weitere Nutzung der Webseite stimmen Sie diesem zu. Unsere Datenschutzerklärung finden Sie hier.