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

Code:
02/2022
Title:
$C^1$-VEM for some variants of the Cahn-Hilliard equation: a numerical exploration
Date:
Sunday 9th January 2022
Author(s):
Antonietti, P.F.; Scacchi, S.; Vacca, G.; Verani, M.
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Abstract:
We consider the $C^1$-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.