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

Abstract

<p style='text-indent:20px;'>We consider the <inline-formula><tex-math id="M2">\begin{document}$ C^1 $\end{document}</tex-math></inline-formula>-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.</p><p style='text-indent:20px;'> </p><p style='text-indent:20px;'>Correction: Bari is added after the zip code 70125 in third author’s address. We apologize for any inconvenience this may cause.</p>