Virtual element methods for parabolic problems on polygonal meshes |
| |
Authors: | Giuseppe Vacca Lourenco Beirão da Veiga |
| |
Institution: | 1. Dipartimento di Matematica, Università degli Studi di Bari, via Orabona 4 ‐ 70125 Bari, Italy;2. Dipartimento di Matematica, Università degli Studi di Milano, via Saldini 50 ‐ 20133 Milano, Italy |
| |
Abstract: | 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 |
| |
Keywords: | virtual elements parabolic problems polygonal meshes |
|
|