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)
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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 |
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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 |
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