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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

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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


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:
  • Jie Shen
  • Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
  • MR Author ID: 257933
  • ORCID: 0000-0002-4885-5732
  • Email:
  • Hongxing Rui
  • Affiliation: School of Mathematics, Shandong University, Jinan 250100, People’s Republic of China
  • MR Author ID: 268523
  • Email:
  • 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:
  • MathSciNet review: 3957886