Author:
Berrone Stefano,Scialò Stefano,Teora Gioana
Abstract
<abstract><p>In this paper, we discuss the accuracy and the robustness of the mixed Virtual Element Methods when dealing with highly anisotropic diffusion problems. In particular, we analyze the performance of different approaches which are characterized by different sets of both boundary and internal degrees of freedom in the presence of a strong anisotropy of the diffusion tensor with constant or variable coefficients. A new definition of the boundary degrees of freedom is also proposed and tested.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
Subject
Applied Mathematics,Mathematical Physics,Analysis
Reference26 articles.
1. Finite Volume Schemes on general grids, for anisotropic and heterogeneous diffusion problems. Available from: https://www.i2m.univ-amu.fr//fvca5//benchmark//Meshes//#mesh4.
2. B. Andreianov, F. Boyer, F. Hubert, Discrete duality finite volume schemes for Leray-Lions type elliptic problems on general 2D meshes, Numer. Meth. Part. Differ. Equ., 23 (2007), 145–195. https://doi.org/10.1002/num.20170
3. O. Angelini, C. Chavant, E. Chénier, R. Eymard, A finite volume scheme for diffusion problems on general meshes applying monotony constraints, SIAM J. Numer. Anal., 47 (2010), 4193–4213. https://doi.org/10.1137/080732183
4. I. Babuška, M. Suri, On locking and robustness in the finite element method, SIAM J. Numer. Anal., 29 (1992), 1261–1293.
5. F. Bassi, L. Botti, A. Colombo, D. A. Di Pietro, P. Tesini, On the flexibility of agglomeration based physical space discontinuous Galerkin discretizations, J. Comput. Phys., 231 (2012), 45–65. https://doi.org/10.1016/j.jcp.2011.08.018