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Title: A posteriori error estimates for the virtual element method
Authors: Cangiani, Andrea
Georgoulis, Emmanuil H.
Pryer, Tristan
Sutton, Oliver J.
First Published: 18-May-2017
Publisher: Springer Verlag (Germany)
Citation: Numerische Mathematik, 2017, pp. 1-37
Abstract: An posteriori error analysis for the virtual element method (VEM) applied to general elliptic problems is presented. The resulting error estimator is of residual-type and applies on very general polygonal/polyhedral meshes. The estimator is fully computable as it relies only on quantities available from the VEM solution, namely its degrees of freedom and element-wise polynomial projection. Upper and lower bounds of the error estimator with respect to the VEM approximation error are proven. The error estimator is used to drive adaptive mesh refinement in a number of test problems. Mesh adaptation is particularly simple to implement since elements with consecutive co-planar edges/faces are allowed and, therefore, locally adapted meshes do not require any local mesh post-processing.
DOI Link: 10.1007/s00211-017-0891-9
ISSN: 0029-599X
eISSN: 0945-3245
Version: Publisher Version
Status: Peer-reviewed
Type: Journal Article
Rights: Copyright © the authors, 2017. This is an open-access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Appears in Collections:Published Articles, Dept. of Mathematics

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