Stability and Convergence Analysis of a Linear Energy Stable Scheme for a Cahn-Hilliard Model with Smooth or Weakly Singular Non-Local Term
Year: 2025
Author: Moumita Mandal, Manisha Chowdhury, Jie Shen
Annals of Applied Mathematics, Vol. 41 (2025), Iss. 2 : pp. 194–218
Abstract
We consider a Cahn-Hilliard gradient flow model with a free energy functional, which contains a non-local term in addition to linear and non-linear local terms. The non-local terms can be based on smooth and weakly singular kernel operators. We establish the well-posedness of this problem, construct an unconditional energy stable scheme, and carry out a stability and convergence analysis. Several numerical results are presented to illustrate the efficiency and robustness of the proposed scheme.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aam.OA-2025-0004
Annals of Applied Mathematics, Vol. 41 (2025), Iss. 2 : pp. 194–218
Published online: 2025-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 25
Keywords: Cahn-Hilliard weakly singular non-local energy stable existence and uniqueness stability and convergence.