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Virtual element methods for parabolic problems on polygonal meshes
Author(s) -
Vacca Giuseppe,
Beirão da Veiga Lourenco
Publication year - 2015
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21982
Subject(s) - polygon mesh , convergence (economics) , mathematics , scheme (mathematics) , volume mesh , element (criminal law) , finite element method , partial differential equation , mathematical optimization , algorithm , mesh generation , geometry , mathematical analysis , structural engineering , engineering , political science , law , economics , economic growth
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