Gradient recovery in adaptive finite element methods for parabolic problems

We derive energy-norm aposteriori error bounds, using gradient recovery (ZZ) estimators to control the spatial error, for fully discrete schemes for the linear heat equation. This appears to be the first completely rigorous derivation of ZZ estimators for fully discrete schemes for evolution problems, without any restrictive assumption on the timestep size. An essential tool for the analysis is the elliptic reconstruction technique.