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.

A C1 virtual element method for the Cahn-Hilliard equation with polygonal meshes / P.F. Antonietti, L. Beirão Da Veiga, S. Scacchi, M. Verani. - In: SIAM JOURNAL ON NUMERICAL ANALYSIS. - ISSN 0036-1429. - 54:1(2016), pp. 34-56.

A C1 virtual element method for the Cahn-Hilliard equation with polygonal meshes

S. Scacchi
Penultimo
;
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.
Cahn-Hilliard equation; virtual element method; numerical analysis
Settore MAT/08 - Analisi Numerica
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/391198
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