Unconditionally energy stable discontinuous Galerkin schemes for the Cahn-Hilliard equation

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:390

Article

Liu, Hailiang¹  Yin, Peimeng² 

[1] Iowa State Univ, Dept Math, Ames, IA 50011 USA

[2] Wayne State Univ, Dept Math, Detroit, MI 48202 USA

关键词: Cahn-Hilliard equation;    Energy dissipation;    Mass conservation;    DG method;    IEQ method;   

DOI  :  10.1016/j.cam.2020.113375

来源: Elsevier

【 摘 要 】

In this paper, we introduce novel discontinuous Galerkin (DG) schemes for the Cahn-Hilliard equation, which arises in many applications. The method is designed by integrating the mixed DG method for the spatial discretization with the Invariant Energy Quadratization (IEQ) approach for the time discretization. Coupled with a spatial projection, the resulting IEQ-DG schemes are shown to be unconditionally energy dissipative, and can be efficiently solved without resorting to any iteration method. Both one and two dimensional numerical examples are provided to verify the theoretical results, and demonstrate the good performance of IEQ-DG in terms of efficiency, accuracy, and preservation of the desired solution properties. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free