Electronic Research Archive

2021, Issue 6: 3629-3647. doi: 10.3934/era.2021054
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A simple virtual element-based flux recovery on quadtree

• Received: 01 November 2020 Revised: 01 June 2021 Published: 22 July 2021
• 65N15, 65N30, 65N50

• In this paper, we introduce a simple local flux recovery for $\mathcal{Q}_k$ 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.

Citation: Shuhao Cao. A simple virtual element-based flux recovery on quadtree[J]. Electronic Research Archive, 2021, 29(6): 3629-3647. doi: 10.3934/era.2021054

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• In this paper, we introduce a simple local flux recovery for $\mathcal{Q}_k$ 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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