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.
Citazione: | 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. |
Tipo: | Articolo in rivista - Articolo scientifico |
Carattere della pubblicazione: | Scientifica |
Presenza di un coautore afferente ad Istituzioni straniere: | No |
Titolo: | A C1 virtual element method for the Cahn-Hilliard equation with polygonal meshes |
Autori: | Antonietti, A; Beirao Da Veiga, L; Scacchi, S; Verani, M |
Autori: | |
Data di pubblicazione: | 2016 |
Lingua: | English |
Rivista: | SIAM JOURNAL ON NUMERICAL ANALYSIS |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1137/15M1008117 |
Appare nelle tipologie: | 01 - Articolo su rivista |