A simple virtual element-based flux recovery on quadtree

<p style='text-indent:20px;'>In this paper, we introduce a simple local flux recovery for <inline-formula><tex-math id="M1">$ \mathcal{Q}_k $</tex-math></inline-formula> finite element of scalar coefficient diffusion equation on quadtree meshes, with no restriction the irregularities hanging nodes. The construction requires specific ad hoc tweaking nodes id="M2">$ l $</tex-math></inline-formula>-irregular (<inline-formula><tex-math id="M3">$ l\geq 2 $</tex-math></inline-formula>) meshes thanks to adoption virtual families. rectangular elements are treated as polygons in context. An efficient <i>a posteriori</i> error estimator is then constructed based recovered flux, and its reliability proved under common assumptions, both which further verified numerics.</p>