$ C^1 $-VEM for some variants of the Cahn-Hilliard equation: A numerical exploration | Zendy

Paola F. Antonietti | Zendy; Simone Scacchi | Zendy; Giuseppe Vacca | Zendy; Marco Verani | Zendy

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$ 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 - 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.

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