  We use the elliptic reconstruction technique in combination with a duality
approach to prove aposteriori error estimates for fully discrete back- ward
Euler scheme for linear parabolic equations. As an application, we com- bine
our result with the residual based estimators from the aposteriori esti- mation
for elliptic problems to derive space-error indicators and thus a fully
practical version of the estimators bounding the error in the L \infty (0, T ;
L2({\Omega})) norm. These estimators, which are of optimal order, extend those
introduced by Eriksson and Johnson (1991) by taking into account the error
induced by the mesh changes and allowing for a more flexible use of the
elliptic estima- tors. For comparison with previous results we derive also an
energy-based aposteriori estimate for the L \infty (0, T ; L2({\Omega}))-error
which simplifies a previous one given in Lakkis and Makridakis (2006). We then
compare both estimators (duality vs. energy) in practical situations and draw
conclusions.
