  We study the long-time behavior of fully discretized semilinear SPDEs with
additive space-time white noise, which admit a unique invariant probability
measure $\mu$. We show that the average of regular enough test functions with
respect to the (possibly non unique) invariant laws of the approximations are
close to the corresponding quantity for $\mu$.
  More precisely, we analyze the rate of the convergence with respect to the
different discretization parameters. Here we focus on the discretization in
time thanks to a scheme of Euler type, and on a Finite Element discretization
in space.
  The results rely on the use of a Poisson equation; we obtain that the rates
of convergence for the invariant laws are given by the weak order of the
discretization on finite time intervals: order $1/2$ with respect to the
time-step and order $1$ with respect to the mesh-size.
