We present a framework that relates preconditioning with a posteriori error estimates in finite element methods. In particular, we use standard tools in subspace correction methods to obtain reliable and efficient error estimators. As a simple example, we recover the classical residual error estimators for the second order elliptic equations.

中文翻译：

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预处理对有限元方法的后验误差估计

我们提出了一种在有限元方法中将预处理与后验误差估计相关的框架。特别是，我们在子空间校正方法中使用标准工具来获得可靠且有效的误差估计量。作为一个简单的例子，我们恢复了二阶椭圆方程的经典残差估计量。