Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 322, Issue -, Pages 783-803Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2016.07.005
Keywords
Cahn-Hilliard equation; Natural element method; Isogeometric analysis; Finite element method; C-1-continuity
Funding
- German Research Foundation (DFG) [STE 544/48-1]
- Cluster of Excellence Engineering of Advanced Materials, Research Area
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The numerical treatment of the fourth-order Cahn-Hilliardequation is nonstandard. Using a Galerkin-method necessitates, for instance, piecewise smooth and globally C-1-continuous basis functions or a mixed formulation. The latter is obtained introducing an auxiliary field which allows to rephrase the Cahn-Hilliardequation 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 C-1-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. (C) 2016 Elsevier Inc. All rights reserved.
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