Title

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

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