In this paper we develop an evolution of the C1 virtual elements of minimal degree for the approximation of the Cahn-Hilliard equation. The proposed method has the advantage of being conforming in H2 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 semidiscrete scheme and investigate the performance of the fully discrete scheme through a set of numerical tests.
Antonietti, A., BEIRAO DA VEIGA, L., Scacchi, S., Verani, M. (2016). A C1 virtual element method for the Cahn-Hilliard equation with polygonal meshes. SIAM JOURNAL ON NUMERICAL ANALYSIS, 54(1), 34-56 [10.1137/15M1008117].
A C1 virtual element method for the Cahn-Hilliard equation with polygonal meshes
BEIRAO DA VEIGA, LOURENCO;
2016
Abstract
In this paper we develop an evolution of the C1 virtual elements of minimal degree for the approximation of the Cahn-Hilliard equation. The proposed method has the advantage of being conforming in H2 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 semidiscrete scheme and investigate the performance of the fully discrete scheme through a set of numerical tests.
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