In this article, we consider a stochastic PDE of parabolic type, driven by a
space-time white-noise, and its numerical discretization in time with a
semi-implicit Euler scheme. When the nonlinearity is assumed to be bounded,
then a dissipativity assumption is satisfied, which ensures that the SDPE
admits a unique invariant probability measure, which is ergodic and strongly
mixing - with exponential convergence to equilibrium. Considering test
functions of class C2, bounded and with bounded derivatives, we
prove that we can approximate this invariant measure using the numerical
scheme, with order 1/2 with respect to the time step