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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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Stability and convergence of second-order schemes for the nonlinear epitaxial growth model without slope selection
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by Zhonghua Qiao, Zhi-zhong Sun and Zhengru Zhang PDF
Math. Comp. 84 (2015), 653-674 Request permission

Abstract:

We present one nonlinear and one linearized numerical schemes for the nonlinear epitaxial growth model without slope selection. Both schemes are proved to be uniquely solvable and convergent with the convergence rate of order two in a discrete $L_2$-norm. By introducing an auxiliary variable in the discrete energy functional, the energy stability of both schemes is guaranteed regardless of the time step size, in the sense that a modified energy is monotonically nonincreasing in discrete time. Numerical experiments are carried out to support the theoretical claims.
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Additional Information
  • Zhonghua Qiao
  • Affiliation: Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong.
  • Email: zqiao@polyu.edu.hk
  • Zhi-zhong Sun
  • Affiliation: Department of Mathematics, Southeast University, Nanjing, 210096, People’s Republic of China.
  • Email: zzsun@seu.edu.cn
  • Zhengru Zhang
  • Affiliation: Laboratory of Mathematics and Complex Systems, Ministry of Education and School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, People’s Republic of China.
  • Email: zrzhang@bnu.edu.cn
  • Received by editor(s): October 13, 2012
  • Received by editor(s) in revised form: June 4, 2013
  • Published electronically: July 17, 2014
  • Additional Notes: The research of the first author was partially supported by the Hong Kong RGC grant PolyU 2021/12P and the Hong Kong Polytechnic University grants A-PL61 and 1-ZV9Y
    The second author was supported by NSFC under Grant 11271068
    The research of the third author was supported by NSFC under Grants 11071124, 11271048, 91130021 and the Fundamental Research Funds for the Central Universities
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 84 (2015), 653-674
  • MSC (2010): Primary 65M06, 65M12, 65Z05
  • DOI: https://doi.org/10.1090/S0025-5718-2014-02874-3
  • MathSciNet review: 3290959