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

详细信息    查看全文

• 作者：S. Kaessmair ^{stefan.kaessmair@ltm.uni-erlangen.de" class="auth_mail" title="E-mail the corresponding author} ; P. Steinmann ; ^{paul.steinmann@ltm.uni-erlangen.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Cahn&ndash ; Hilliard equation ; Natural element method ; Isogeometric analysis ; Finite element method ; C1C1-continuity
• 刊名：Journal of Computational Physics
• 出版年：2016
• 出版时间：1 October 2016
• 年：2016
• 卷：322
• 期：Complete
• 页码：783-803
• 全文大小：2024 K

文摘

The numerical treatment of the fourth-order Cahn–Hilliard equation is nonstandard. Using a Galerkin  -method necessitates, for instance, piecewise smooth and globally C¹$C^1$-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$C^1$-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.