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arXiv · 1502.03259

A $C^1$ virtual element method for the Cahn-Hilliard equation with polygonal meshes

Paola F. Antonietti·Lourenco Beirao da Veiga·Simone Scacchi·Marco Verani
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Abstract

In this paper we develop an evolution of the $C^1$ virtual elements of minimal degree for the approximation of the Cahn-Hilliard equation. The proposed method has the advantage of being conforming in $H^2$ and making use of a very simple set of degrees of freedom, namely 3 degrees of freedom per vertex of the mesh. Moreover, although the present method is new also on triangles, it can make use of general polygonal meshes. As a theoretical and practical support, we prove the convergence of the semi-discrete scheme and investigate the performance of the fully discrete scheme through a set of numerical tests.

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Paola F. Antonietti, Lourenco Beirao da Veiga, Simone Scacchi, Marco Verani. 2015-02-11. A $C^1$ virtual element method for the Cahn-Hilliard equation with polygonal meshes. https://arxiv.org/abs/1502.03259

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