Phase-field dynamics with transfer of materials: The Cahn-Hillard equation with reaction rate dependent dynamic boundary conditions

Patrik Knopf*, Kei Fong LAM, Chun Liu, Stefan Metzger

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

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.

Original languageEnglish
Pages (from-to)229-282
Number of pages54
JournalESAIM: Mathematical Modelling and Numerical Analysis
Volume55
Issue number1
DOIs
Publication statusPublished - 18 Feb 2021

Scopus Subject Areas

  • Analysis
  • Numerical Analysis
  • Modelling and Simulation
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Cahn-Hilliard equation
  • Dynamic boundary conditions
  • Finite element analysis
  • Gradient flow
  • Relaxation by Robin boundary conditions

Fingerprint

Dive into the research topics of 'Phase-field dynamics with transfer of materials: The Cahn-Hillard equation with reaction rate dependent dynamic boundary conditions'. Together they form a unique fingerprint.

Cite this