Energy stability and convergence of SAV block-centered finite difference method for gradient flows
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Abstract:
We present in this paper construction and analysis of a block-centered finite difference method for the spatial discretization of the scalar auxiliary variable Crank-Nicolson scheme (SAV/CN-BCFD) for gradient flows, and show rigorously that the scheme is second-order in both time and space in various discrete norms. When equipped with an adaptive time strategy, the SAV/CN-BCFD scheme is accurate and extremely efficient. Numerical experiments on typical Allen-Cahn and Cahn-Hilliard equations are presented to verify our theoretical results and to show the robustness and accuracy of the SAV/CN-BCFD scheme.References
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Additional Information
- Xiaoli Li
- Affiliation: School of Mathematics, Shandong University, Jinan 250100, People’s Republic of China
- Address at time of publication: Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific Computing and School of Mathematical Sciences, Xiamen University, Xiamen, Fujian, 361005, People’s Republic of China
- MR Author ID: 1152951
- Email: xiaolisdu@163.com
- Jie Shen
- Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
- MR Author ID: 257933
- ORCID: 0000-0002-4885-5732
- Email: shen7@purdue.edu
- Hongxing Rui
- Affiliation: School of Mathematics, Shandong University, Jinan 250100, People’s Republic of China
- MR Author ID: 268523
- Email: hxrui@sdu.edu.cn
- Received by editor(s): June 26, 2018
- Received by editor(s) in revised form: November 18, 2018
- Published electronically: April 1, 2019
- Additional Notes: The first author thanks the China Scholarship Council for financial support.
The work of the second author was supported in part by NSF grants DMS-1620262, DMS-1720442, and AFOSR grant FA9550-16-1-0102.
The second author is the corresponding author.
The work of the third author was supported by the National Natural Science Foundation of China grant 11671233. - © Copyright 2019 American Mathematical Society
- Journal: Math. Comp. 88 (2019), 2047-2068
- MSC (2010): Primary 65M06, 65M12, 65M15, 35K20, 35K35, 65Z05
- DOI: https://doi.org/10.1090/mcom/3428
- MathSciNet review: 3957886