A posteriori error estimates for the virtual element method

Cangiani, A., Georgoulis, E. H., Pryer, T. and Sutton, O. J. (2017) A posteriori error estimates for the virtual element method. Numerische Mathematik, 137 (4). pp. 857-893. ISSN 0029-599X doi: 10.1007/s00211-017-0891-9

Abstract/Summary

An a 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.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/70444
Identification Number/DOI	10.1007/s00211-017-0891-9
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	Springer
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