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In this paper, we determine the convergence speed of an upscaling of apseudo-parabolic system containing drift terms with scale separation of size$\epsilon \ll 1$. Both the upscaling and convergence speed determinationexploit a natural spatial-temporal decomposition, which splits thepseudo-parabolic system into a spatial elliptic partial differential equationand a temporal ordinary differential equation. We extend the applicability tospace-time domains that are a product of spatial and temporal domains, such asa time-independent perforated spatial domain. Finally, for special cases weshow convergence speeds for global times, i.e. $t \in \mathbf{R}_+$, by usingtime intervals that converge to $\mathbf{R}_+$ as $\epsilon\downarrow 0$.

Homogenization of a pseudo-parabolic system via a spatial-temporal decoupling: upscaling and corrector estimates for perforated domains