Loading [MathJax]/jax/output/HTML-CSS/config.js
Volume 41, Issue 2
Stability and Convergence Analysis of a Linear Energy Stable Scheme for a Cahn-Hilliard Model with Smooth or Weakly Singular Non-Local Term

Moumita Mandal, Manisha Chowdhury & Jie Shen

Ann. Appl. Math., 41 (2025), pp. 194-218.

Published online: 2025-06

Export citation
  • 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.

  • AMS Subject Headings

65M12, 65M70, 35K35, 35K61

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{AAM-41-194, author = {Mandal , MoumitaChowdhury , Manisha and Shen , Jie}, title = {Stability and Convergence Analysis of a Linear Energy Stable Scheme for a Cahn-Hilliard Model with Smooth or Weakly Singular Non-Local Term}, journal = {Annals of Applied Mathematics}, year = {2025}, volume = {41}, number = {2}, pages = {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.

}, issn = {}, doi = {https://doi.org/10.4208/aam.OA-2025-0004}, url = {http://global-sci.org/intro/article_detail/aam/24148.html} }
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 -

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.

Mandal , MoumitaChowdhury , Manisha and Shen , Jie. (2025). Stability and Convergence Analysis of a Linear Energy Stable Scheme for a Cahn-Hilliard Model with Smooth or Weakly Singular Non-Local Term. Annals of Applied Mathematics. 41 (2). 194-218. doi:10.4208/aam.OA-2025-0004
Copy to clipboard
The citation has been copied to your clipboard