A stable second-order BDF scheme for the three-dimensional Cahn-Hilliard-Hele-Shaw system
- Authors
- Li, Yibao; Yu, Qian; Fang, Weiwei; Xia, Binhu; Kim, Junseok
- Issue Date
- 12-1월-2021
- Publisher
- SPRINGER
- Keywords
- Backward differentiation formula; Cahn-Hilliard-Hele-Shaw; Unique solvability; Linear multigrid; Second-order accuracy
- Citation
- ADVANCES IN COMPUTATIONAL MATHEMATICS, v.47, no.1
- Indexed
- SCIE
SCOPUS
- Journal Title
- ADVANCES IN COMPUTATIONAL MATHEMATICS
- Volume
- 47
- Number
- 1
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/50123
- DOI
- 10.1007/s10444-020-09835-6
- ISSN
- 1019-7168
- Abstract
- We propose a stable scheme to solve numerically the Cahn-Hilliard-Hele-Shaw system in three-dimensional space. In the proposed scheme, we discretize the space and time derivative terms by combining with backward differentiation formula, which turns out to be both second-order accurate in space and time. Using this method, a set of linear elliptic equations are solved instead of the complicated and high-order nonlinear equations. We prove that our proposed scheme is uniquely solvable. We use a linear multigrid solver, which is fast and convergent, to solve the resulting discrete system. The numerical tests indicate that our scheme can use a large time step. The accuracy and other capability of the proposed algorithm are demonstrated by various computational results.
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