A stable and structure-preserving scheme for a non-local Allen–Cahn equation

We propose a stable and structure-preserving finite difference scheme for a non-local Allen–Cahn equation which describes a process of phase separation in a binary mixture. The proposed scheme inherits characteristic properties, the conservation of mass and the decrease of the global energy from the...

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Bibliographic Details
Published inJapan journal of industrial and applied mathematics Vol. 35; no. 3; pp. 1245 - 1281
Main Author Okumura, Makoto
Format Journal Article
LanguageEnglish
Published Tokyo Springer Japan 01.11.2018
Springer Nature B.V
Subjects
Applications of Mathematics
Binary mixtures
Computational Mathematics and Numerical Analysis
Energy conservation
Finite difference method
Mathematics
Mathematics and Statistics
Original Paper
Phase separation
Non-local Allen–Cahn equation
65M06
Discrete variational derivative method
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Summary:We propose a stable and structure-preserving finite difference scheme for a non-local Allen–Cahn equation which describes a process of phase separation in a binary mixture. The proposed scheme inherits characteristic properties, the conservation of mass and the decrease of the global energy from the equation. We show the stability and unique existence of the solution of the scheme. We also prove the error estimate for the scheme. Numerical experiments demonstrate the effectiveness of the proposed scheme.
ISSN:0916-7005
1868-937X
DOI:10.1007/s13160-018-0326-8