Analysis of a novel finite element method for a modified Cahn-Hilliard-Hele-Shaw system

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:376

Article

Jia, Hongen¹  Guo, Yayu¹  Li, Jichun²  Huang, Yunqing³ 

[1] Taiyuan Univ Technol, Coll Math, Taiyuan 030024, Peoples R China

[2] Univ Nevada, Dept Math Sci, Las Vegas, NV 89154 USA

[3] Xiangtan Univ, Hunan Key Lab Computat & Simulat Sci & Engn, Xiangtan, Peoples R China

关键词: Modified Cahn-Hilliard equation;    Hele-Shaw cell;    Convex splitting;    Energy stability;    Unconditionally stable;   

DOI  :  10.1016/j.cam.2020.112846

来源: Elsevier

【 摘 要 】

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. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free