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

12/31/2021

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by   Paola F. Antonietti, et al.

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University of Bari Aldo Moro

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Politecnico di Milano

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Università degli Studi di Milano

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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.