We consider the C1-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.
C1-VEM for some variants of the Cahn-Hilliard equation: A numerical exploration / P.F. Antonietti, S. Scacchi, G. Vacca, M. Verani. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S. - ISSN 1937-1632. - 15:8(2022 Aug), pp. 1919-1939. [10.3934/dcdss.2022038]
C1-VEM for some variants of the Cahn-Hilliard equation: A numerical exploration
S. ScacchiSecondo
;M. VeraniUltimo
2022
Abstract
We consider the C1-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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10.3934_dcdss.2022038.pdf
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