Käßmair S, Steinmann P (2016)
Publication Type: Journal article
Publication year: 2016
Book Volume: 322
Pages Range: 783-803
DOI: 10.1016/j.jcp.2016.07.005
The numerical treatment of the fourth-order Cahn--Hilliard equation is nonstandard. Using a Galerkin -method necessitates, for instance, piecewise smooth and globally C1-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 C1-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.
APA:
Käßmair, S., & Steinmann, P. (2016). Comparative computational analysis of the Cahn--Hilliard equation with emphasis on C1-continuous methods. Journal of Computational Physics, 322, 783-803. https://doi.org/10.1016/j.jcp.2016.07.005
MLA:
Käßmair, Stefan, and Paul Steinmann. "Comparative computational analysis of the Cahn--Hilliard equation with emphasis on C1-continuous methods." Journal of Computational Physics 322 (2016): 783-803.
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