Virtual element methods for parabolic problems on polygonal meshes. Issue 6 (3rd July 2015)

• Record Type: Journal Article
• Authors: Vacca, Giuseppe; Beirão da Veiga, Lourenco
• Is Part Of: Numerical methods for partial differential equations. Volume 31:Issue 6(2015)
• Page Start: 2110
• Page End: 2134
• Publication Date: 2015-07-03
• Subjects: Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.21982
• Languages: English
• ISSNs: 0749-159X

Abstract

<abstract abstract-type="main"> <title> <x xml:space="preserve">Abstract</x> </title> <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</p> </abstract>