A $C^1$ virtual element method for the Cahn-Hilliard equation with polygonal meshes
Numerical Analysis
2015-02-12 v1
Abstract
In this paper we develop an evolution of the virtual elements of minimal degree for the approximation of the Cahn-Hilliard equation. The proposed method has the advantage of being conforming in 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.
Cite
@article{arxiv.1502.03259,
title = {A $C^1$ virtual element method for the Cahn-Hilliard equation with polygonal meshes},
author = {Paola F. Antonietti and Lourenco Beirao da Veiga and Simone Scacchi and Marco Verani},
journal= {arXiv preprint arXiv:1502.03259},
year = {2015}
}