We derive a posteriori bounds for
(
V
−
V
^
)
(V - \hat V)
and its difference quotient
(
V
−
V
^
)
x
{(V - \hat V)_x}
, where
V
V
and
V
^
\hat V
are, respectively, the exact and computed solution of a difference approximation to a mildly nonlinear parabolic initial boundary problem, with a known steadystate solution. It is assumed that the computation is over a long interval of time. The estimates are valid for a class of difference approximations, which includes the CrankNicolson method, and are of the same magnitude for both
(
V
−
V
^
)
(V - \hat V)
and
(
V
−
V
^
)
x
(V - \hat V)x
.