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Title: A simple virtual element-based flux recovery on quadtree

In this paper, we introduce a simple local flux recovery for \begin{document}$ \mathcal{Q}_k $\end{document} finite element of a scalar coefficient diffusion equation on quadtree meshes, with no restriction on the irregularities of hanging nodes. The construction requires no specific ad hoc tweaking for hanging nodes on \begin{document}$ l $\end{document}-irregular (\begin{document}$ l\geq 2 $\end{document}) meshes thanks to the adoption of virtual element families. The rectangular elements with hanging nodes are treated as polygons as in the flux recovery context. An efficient a posteriori error estimator is then constructed based on the recovered flux, and its reliability is proved under common assumptions, both of which are further verified in numerics.

 
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Award ID(s):
2136075
NSF-PAR ID:
10342824
Author(s) / Creator(s):
Date Published:
Journal Name:
Electronic Research Archive
Volume:
29
Issue:
6
ISSN:
2688-1594
Page Range / eLocation ID:
3629
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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