Lower a posteriori error bounds obtained using the standard bubble function approach are reviewed in the context of anisotropic meshes. A numerical example is given that clearly demonstrates that the short-edge jump residual terms in such bounds are not sharp. Hence, for linear finite element approximations of the Laplace equation in polygonal domains, a new approach is employed to obtain essentially sharper lower a posteriori error bounds and thus to show that the upper error estimator in the recent paper [N. Kopteva, Numer. Math., 137 (2017), 607-642] is efficient on certain anisotropic meshes.

中文翻译：

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降低各向异性网格的后验误差估计

在各向异性网格的上下文中审查使用标准气泡函数方法获得的较低的后验误差界限。给出了一个数值例子，清楚地表明在这样的边界内的短边跳跃残差项并不尖锐。因此，对于多边形域中拉普拉斯方程的线性有限元近似，采用了一种新方法来获得本质上更清晰的后验误差下限，从而表明最近论文 [N. 科普特娃，数字。Math., 137 (2017), 607-642] 在某些各向异性网格上是有效的。