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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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Why large time-stepping methods for the Cahn-Hilliard equation is stable
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by Dong Li HTML | PDF
Math. Comp. 91 (2022), 2501-2515 Request permission

Abstract:

We consider the Cahn-Hilliard equation with standard double-well potential. We employ a prototypical class of first order in time semi-implicit methods with implicit treatment of the linear dissipation term and explicit extrapolation of the nonlinear term. When the dissipation coefficient is held small, a conventional wisdom is to add a judiciously chosen stabilization term in order to afford relatively large time stepping and speed up the simulation. In practical numerical implementations it has been long observed that the resulting system exhibits remarkable stability properties in the regime where the stabilization parameter is $\mathcal O(1)$, the dissipation coefficient is vanishingly small and the size of the time step is moderately large. In this work we develop a new stability theory to address this perplexing phenomenon.
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Additional Information
  • Dong Li
  • Affiliation: SUSTech International Center for Mathematics, and Department of Mathematics, Southern University of Science and Technology, Shenzhen, People’s Republic of China
  • MR Author ID: 723577
  • ORCID: 0000-0003-2367-4764
  • Email: lid@sustech.edu.cn
  • Received by editor(s): March 3, 2022
  • Received by editor(s) in revised form: March 20, 2022, April 2, 2022, and May 22, 2022
  • Published electronically: July 28, 2022
  • © Copyright 2022 American Mathematical Society
  • Journal: Math. Comp. 91 (2022), 2501-2515
  • MSC (2020): Primary 35Q35
  • DOI: https://doi.org/10.1090/mcom/3768
  • MathSciNet review: 4473094