Phase-field dynamics with transfer of materials: The Cahn–Hillard equation with reaction rate dependent dynamic boundary conditions
Knopf P, Lam KF, Liu C, Metzger S (2021)
Publication Type: Journal article, Original article
Publication year: 2021
Journal
Book Volume: 55
Pages Range: 229-282
Issue: 1
DOI: 10.1051/m2an/2020090
Abstract
The Cahn–Hilliard equation is one of the most common models to describe phase separation processes of a mixture of two materials. For a better description of short-range interactions between the material and the boundary, various dynamic boundary conditions for the Cahn–Hilliard equation have been proposed and investigated in recent times. Of particular interests are the model by Goldstein et al. [Phys. D 240 (2011) 754–766] and the model by Liu and Wu [Arch. Ration. Mech. Anal. 233 (2019) 167–247]. Both of these models satisfy similar physical properties but differ greatly in their mass conservation behaviour. In this paper we introduce a new model which interpolates between these previous models, and investigate analytical properties such as the existence of unique solutions and convergence to the previous models mentioned above in both the weak and the strong sense. For the strong convergences we also establish rates in terms of the interpolation parameter, which are supported by numerical simulations obtained from a fully discrete, unconditionally stable and convergent finite element scheme for the new interpolation model.
Authors with CRIS profile
Stefan Metzger
Professur für Angewandte Mathematik (Analysis und Numerik partieller Differentialgleichungen)
Involved external institutions
Illinois Institute of Technology
United States (USA) (US)
Universität Regensburg
Germany (DE)
Hong Kong Baptist University (HKBU) / 香港浸會大學
China (CN)
United States (USA) (US)
Universität Regensburg
Germany (DE)
Hong Kong Baptist University (HKBU) / 香港浸會大學
China (CN)
How to cite
APA:
Knopf, P., Lam, K.F., Liu, C., & Metzger, S. (2021). Phase-field dynamics with transfer of materials: The Cahn–Hillard equation with reaction rate dependent dynamic boundary conditions. Mathematical Modelling and Numerical Analysis, 55, 229-282. https://doi.org/10.1051/m2an/2020090
MLA:
Knopf, Patrik, et al. "Phase-field dynamics with transfer of materials: The Cahn–Hillard equation with reaction rate dependent dynamic boundary conditions." Mathematical Modelling and Numerical Analysis 55 (2021): 229-282.
BibTeX: Download