Codice | 12/2015 |
Titolo | A $C^1$ virtual element method for the Cahn-Hilliard equation with polygonal meshes |
Data | 2015-03-16 |
Autore/i | Antonietti, P. F.; Beirao da Veiga, L.; Scacchi, S.; Verani, M. |
Link | Download full text |
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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