In this article, we consider recovery-based a posteriori error estimators for the Virtual Element Method (VEM) and the Boundary Element Method based Finite Element Method (BEM-based FEM). Both methods are Galerkin methods on polygonal and polyhedral grids for the numerical solution of partial differential equations. Thus, they are highly flexible and particularly efficient in combination with adaptive refinement. Our error estimator computes the distance between the finite element gradient and its post-processed version to obtain an accurate approximation of the true error. The post-processing is realised by local averaging and is therefore easy to implement and fast. Furthermore, we have found points of extraordinary accuracy, so called stress points, on specific regular elements for the BEM-based FEM. We demonstrate that, when sampling these stress points, the recovered gradient becomes superconvergent, which means that it converges at a greater rate than the unprocessed gradient.

在本文中，我们考虑基于恢复的后验误差估计器，用于虚拟元素方法（VEM）和基于边界元素方法的有限元方法（基于BEM的FEM）。对于偏微分方程的数值解，这两种方法都是在多边形和多面网格上的Galerkin方法。因此，它们具有高度的灵活性，并与自适应改进相结合特别有效。我们的误差估算器计算有限元梯度与其后处理版本之间的距离，以获得真实误差的精确近似值。后处理通过局部平均来实现，因此易于实现且速度很快。此外，我们在基于BEM的FEM的特定常规元素上发现了非凡的精度点，即所谓的应力点。我们证明，