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Medientyp: E-Artikel Titel: Virtual element methods for parabolic problems on polygonal meshes Beteiligte: Vacca, Giuseppe; Beirão da Veiga, Lourenco Erschienen: Wiley, 2015 Erschienen in: Numerical Methods for Partial Differential Equations Sprache: Englisch DOI: 10.1002/num.21982 ISSN: 0749-159X; 1098-2426 Entstehung: Anmerkungen: Beschreibung: <jats:p>The virtual element method (VEM) is a recent technology that can make use of very general polygonal/polyhedral meshes without the need to integrate complex nonpolynomial functions on the elements and preserving an optimal order of convergence. In this article, we develop for the first time, the VEM for parabolic problems on polygonal meshes, considering time‐dependent diffusion as our model problem. After presenting the scheme, we develop a theoretical analysis and show the practical behavior of the proposed method through a large array of numerical tests. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 2110–2134, 2015</jats:p>