论文标题
Quadtree上简单的基于虚拟元素的通量恢复
A simple virtual element-based flux recovery on quadtree
论文作者
论文摘要
在本文中，我们引入了一个简单的局部通量恢复，用于$ \ Mathcal {q} _K $在Quadtree网格上的标量系数扩散方程的有限元，对悬挂节点的不规则性无限制。由于采用了虚拟元素家族，该构造不需要在$ l $ irronformular（$ l \ geq 2 $）网格上悬挂节点的特定临时调整。带有悬挂节点的矩形元素被视为多边形，如通量恢复环境中。然后根据恢复的通量构建了有效的后验误差估计器，并在共同的假设下证明了其可靠性，这两者在数字中都得到了进一步验证。
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.
