In this paper, we introduce a simple local flux recovery for Q_k 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 l-irregular (l\geq 2) meshes thanks to the adoption of some novel ideas borrowed from 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 projected to a space with simpler structure , and its reliability is proved under common assumptions, both of which are further verified in numerics.
In this paper, we introduce a simple local flux recovery for Q_k 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 l-irregular (l\geq 2) 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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some novel ideas borrowed from
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projected to a space with simpler structure