TY - JOUR
T1 - Stability and Convergence Analysis of a Linear Energy Stable Scheme for a Cahn-Hilliard Model with Smooth or Weakly Singular Non-Local Term
AU - Mandal , Moumita
AU - Chowdhury , Manisha
AU - Shen , Jie
JO - Annals of Applied Mathematics
VL - 2
SP - 194
EP - 218
PY - 2025
DA - 2025/06
SN - 41
DO - http://doi.org/10.4208/aam.OA-2025-0004
UR - https://global-sci.org/intro/article_detail/aam/24148.html
KW - Cahn-Hilliard, weakly singular, non-local, energy stable, existence and
uniqueness, stability and convergence.
AB - <p style="text-align: justify;">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.</p>