Volume 49, Number 2, March-April 2015
|Page(s)||577 - 599|
|Published online||17 March 2015|
Residual a posteriori error estimation for the Virtual Element Method for elliptic problems
Dipartimento di Matematica “F. Enriques”, Università degli Studi
di Milano, via Saldini
2 Applied Mathematics and Plasma Physics Group, Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
3 IMATI del CNR, via Ferrata 1, 27100 Pavia, Italy
Received: 3 November 2013
Revised: 30 June 2014
A posteriori error estimation and adaptivity are very useful in the context of the virtual element and mimetic discretization methods due to the flexibility of the meshes to which these numerical schemes can be applied. Nevertheless, developing error estimators for virtual and mimetic methods is not a straightforward task due to the lack of knowledge of the basis functions. In the new virtual element setting, we develop a residual based a posteriori error estimator for the Poisson problem with (piecewise) constant coefficients, that is proven to be reliable and efficient. We moreover show the numerical performance of the proposed estimator when it is combined with an adaptive strategy for the mesh refinement.
Mathematics Subject Classification: 65N30
Key words: A posteriori error estimation / virtual element method / polygonal mesh / high-order scheme
© EDP Sciences, SMAI, 2015
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.