Open Access$ C^1 $-VEM for some variants of the Cahn-Hilliard equation: A numerical exploration
Author(s) -
Paola F. Antonietti,
Simone Scacchi,
Giuseppe Vacca,
Marco Verani
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series s
Language(s) - English
Resource type - Journals
eISSN - 1937-1632
pISSN - 1937-1179
DOI - 10.3934/dcdss.2022038
Subject(s) - discretization , polygon mesh , focus (optics) , cahn–hilliard equation , mathematics , inpainting , computer science , discrete mathematics , mathematical analysis , geometry , partial differential equation , physics , artificial intelligence , optics , image (mathematics)
We consider the \begin{document}$ C^1 $\end{document} -Virtual Element Method (VEM) for the conforming numerical approximation of some variants of the Cahn-Hilliard equation on polygonal meshes. In particular, we focus on the discretization of the advective Cahn-Hilliard problem and the Cahn-Hilliard inpainting problem. We present the numerical approximation and several numerical results to assess the efficacy of the proposed methodology.