Numerical Analysis for the Cahn-Hilliard-Hele-Shaw System with Variable Mobility and Logarithmic Flory-Huggins Potential
Document Type
Article
Publication Date
10-9-2019
Publication Title
Applied Numerical Mathematics
Abstract
In this paper, a fully discrete scheme is proposed for solving the Cahn-Hilliard-Hele-Shaw system with a logarithmic potential and concentration dependent mobility. Using the regularization procedure, the domain for the logarithmic free energy density function F(ϕ) is extended from (−1,1) to (−∞,∞). A convex-splitting method of the energy is adopted in time and the mixed finite element method is used in space. Furthermore, we prove the stability of the proposed numerical method and establish the optimal error estimate in the energy norm. Finally, numerical results are presented to support our theoretical analysis.
Keywords
Logarithmic potential; Cahn-Hilliard-Hele-Shaw; Regularized functional; Concentration dependent mobility
Disciplines
Applied Mathematics | Numerical Analysis and Computation | Physical Sciences and Mathematics
Language
English
Repository Citation
Guo, Y.,
Jia, H.,
Li, J.,
Li, M.
(2019).
Numerical Analysis for the Cahn-Hilliard-Hele-Shaw System with Variable Mobility and Logarithmic Flory-Huggins Potential.
Applied Numerical Mathematics
http://dx.doi.org/10.1016/j.apnum.2019.09.014