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In this article, we consider a stochastic PDE of parabolic type, driven by aspace-time white-noise, and its numerical discretization in time with asemi-implicit Euler scheme. When the nonlinearity is assumed to be bounded,then a dissipativity assumption is satisfied, which ensures that the SDPEadmits a unique invariant probability measure, which is ergodic and stronglymixing - with exponential convergence to equilibrium. Considering testfunctions of class $\mathcal{C}^2$, bounded and with bounded derivatives, weprove that we can approximate this invariant measure using the numericalscheme, with order 1/2 with respect to the time step.

Approximation of the invariant measure with an Euler scheme for Stochastic PDE's driven by Space-Time White Noise