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| Stability and Convergence Analysis ofa Linear Energy Stable Scheme for aCahn-Hilliard Model with Smooth orWeakly Singular Non-local Term |
| Moumita Mandal,Manisha Chowdhur,Jie Shen |
| (Department of Mathematics, Indian Institute of Technology Jodhpur,
Rajasthan 342 030, India;School of Mathematical Science, Eastern Institute of Technology, Ningbo,
Zhejiang 315200, China) |
| DOI： |
| 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. |
| Key words: Cahn-Hilliard, weakly singular, non-local, energy stable, existence and
uniqueness, stability and convergence. |