Journal
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Volume 353, Issue -, Pages 38-48Publisher
ELSEVIER
DOI: 10.1016/j.cam.2018.12.024
Keywords
Allen-Cahn equation; Finite element method; Energy stable; Error estimation
Categories
Funding
- Hunan Provincial Innovation Foundation for Postgraduate, PR China [CX2016B247]
- NSFC, PR China Project [91430213]
- NSFC Project, PR China [11671341]
- Department of Education of Hunan Province Project, PR China [16A206]
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In this paper, we design, analyze and numerically validate an unconditionally energy stable second order numerical method for solving the Allen-Cahn equation which represents a model for anti-phase domain coarsening in a binary alloy. The proposed scheme inherits the property of the decrease of the total energy from the Allen-Cahn equation. An error estimate for the fully discretized scheme is also established. Numerical examples are presented to confirm the accuracy, efficiency, and stability of the proposed method. In particular, the method is shown to be unconditionally energy stable and second order accurate in both time and space discretizations. (C) 2018 Elsevier B.V. All rights reserved.
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