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A posteriori error estimates for the virtual element method

Cangiani, Andrea; Georgoulis, Emmanuil H.; Pryer, Tristan; Sutton, Oliver J.

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Authors

Andrea Cangiani

Emmanuil H. Georgoulis

Tristan Pryer

Oliver J. Sutton



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.

Citation

Cangiani, A., Georgoulis, E. H., Pryer, T., & Sutton, O. J. (2017). A posteriori error estimates for the virtual element method. Numerische Mathematik, 137(4), 857-893. https://doi.org/10.1007/s00211-017-0891-9

Journal Article Type Article
Acceptance Date Jan 17, 2017
Online Publication Date May 18, 2017
Publication Date 2017-12
Deposit Date Aug 9, 2019
Publicly Available Date Aug 9, 2019
Journal Numerische Mathematik
Print ISSN 0029-599X
Electronic ISSN 0945-3245
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
Volume 137
Issue 4
Pages 857-893
DOI https://doi.org/10.1007/s00211-017-0891-9
Public URL https://nottingham-repository.worktribe.com/output/2411426
Publisher URL https://link.springer.com/article/10.1007%2Fs00211-017-0891-9
Contract Date Aug 9, 2019

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