Title

Analysis of a Novel Finite Element Method for a Modified Cahn–Hilliard–Hele–Shaw System

Document Type

Article

Publication Date

3-14-2020

Publication Title

Journal of Computational and Applied Mathematics

Volume

376

First page number:

1

Last page number:

13

Abstract

In this paper, a novel finite element method for solving a modified Cahn–Hilliard–Hele–Shaw system is proposed. The time discretization is based on the convex splitting of the energy functional in the modified Cahn–Hilliard equation, i.e., the high-order nonlinear term and the linear term in the chemical potential are treated explicitly and implicitly, respectively. Designing in this way leads to solving a linear system at each time step, which is much efficient compared to solving a nonlinear system resulting from most existing schemes. The proposed scheme is proved to be unconditionally energy stable and optimally convergent for the phase variable. Numerical results are presented to support our theoretical analysis.

Keywords

Modified Cahn–Hilliard equation; Hele–Shaw cell; Convex splitting; Energy stability; Unconditionally stable

Disciplines

Applied Mathematics | Energy Systems

Language

English

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