A simple virtual element-based flux recovery on quadtree
A simple virtual element-based flux recovery on quadtree
复制标题
DOI：
10.3934/era.2021054
复制
发表时间：
2020-06
影响因子：
0.8
通讯作者：
Shuhao Cao
中科院分区：
文献类型：
--
作者：
Shuhao Cao
本文在四叉树网格上对一类标量系数扩散方程的\开始{document}$ \mathcal{Q}_k $\end{document}有限元引入了一种简单的局部通量恢复方法，对悬挂节点的不规则性没有限制。由于采用了虚拟元素族，因此该构造不需要对\开始{document}$ l $\end{document}-不规则（\开始{document}$ l\geq 2 $\end{document}）网格上的挂起节点进行特定的特殊调整。在通量恢复上下文中，具有悬挂节点的矩形单元被视为多边形。然后基于恢复的磁通量构造了一个有效的后验误差估计器，并在一般假设下证明了其可靠性，数值上进一步验证了这两种方法。
In this paper, we introduce a simple local flux recovery for \begin{document}$ \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.