Comparative computational analysis of the Cahn-Hilliard equation with emphasis on C1-continuous methods

Kaessmair, S. and Steinmann, P. (2016) Comparative computational analysis of the Cahn-Hilliard equation with emphasis on C1-continuous methods. Journal of Computational Physics, 322, pp. 783-803. (doi: 10.1016/j.jcp.2016.07.005)

Full text not currently available from Enlighten.

Abstract

The numerical treatment of the fourth-order Cahn–Hilliard equation is nonstandard. Using a Galerkin-method necessitates, for instance, piecewise smooth and globally -continuous basis functions or a mixed formulation. The latter is obtained introducing an auxiliary field which allows to rephrase the Cahn–Hilliard equation as a set of two coupled second-order equations. In view of this, the formulation in terms of the primal unknown appears to be a more intuitive and natural choice but requires a -continuous interpolation. Therefore, isogeometric analysis, using a spline basis, and natural element analysis are addressed in the present contribution. Mixed second-order finite element methods introducing the chemical potential or alternatively a nonlocal concentration as auxiliary field serve as references to which both higher-order methods are compared in terms of accuracy and efficiency.

Item Type:Articles
Additional Information:Supported by funding from : German Research Foundation (DFG) under grant STE 544/48-1 and the Cluster of Excellence “Engineering of Advanced Materials”, Research Area A3.
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Steinmann, Professor Paul
Authors: Kaessmair, S., and Steinmann, P.
College/School:College of Science and Engineering > School of Engineering > Infrastructure and Environment
Journal Name:Journal of Computational Physics
Publisher:Elsevier
ISSN:0021-9991
ISSN (Online):1090-2716
Published Online:12 July 2016

University Staff: Request a correction | Enlighten Editors: Update this record