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.
Articolo in rivista - Articolo scientifico
Cahn-Hilliard equation; Virtual element method;
Chan-Hilliard equation, polygonal meshes, virtual elements
English
34
56
23
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].
Antonietti, A; BEIRAO DA VEIGA, L; Scacchi, S; Verani, M
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/138475
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