A simple virtual element-based flux recovery on quadtree

Abstract

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 ($l\ge 2$) 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.

References in corpus (2)

• Anisotropic Error Estimates of The Linear Nonconforming Virtual Element Methods
• A Recovery-Based A Posteriori Error Estimator for H(curl) Interface Problems