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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Energy stability and convergence of SAV block-centered finite difference method for gradient flows
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by Xiaoli Li, Jie Shen and Hongxing Rui HTML | PDF
Math. Comp. 88 (2019), 2047-2068 Request permission

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.
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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