Open AccessA simple virtual element-based flux recovery on quadtree
Author(s) -
Shuhao Cao
Publication year - 2021
Publication title -
electronic research archive
Language(s) - English
Resource type - Journals
ISSN - 2688-1594
DOI - 10.3934/era.2021054
Subject(s) - mathematics , polygon mesh , context (archaeology) , scalar (mathematics) , combinatorics , simple (philosophy) , estimator , discrete mathematics , geometry , statistics , paleontology , philosophy , epistemology , biology
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.