We derive aposteriori error estimates for fully discrete approximations to solutions of linear parabolic equations on the space-time domain. The space discretization uses finite element spaces, that are allowed to change in time. Our main tool is an appropriate adaptation of the elliptic reconstruction technique, introduced by Makridakis and Nochetto (2003). We derive novel optimal order aposteriori error estimates for the maximum-in-time and mean-square-in-space norm and the mean-square in space-time of the time-derivative norm.

翻译：本文推导了时空域上线性抛物方程全离散近似解的后验误差估计。空间离散采用有限元空间，并允许其随时间变化。我们的主要工具是对Makridakis与Nochetto（2003）提出的椭圆重构技术进行适当改进。针对时间导数范数的最大时间-均方空间范数及时空均方范数，我们推导了具有最优阶的新型后验误差估计。