  We consider cosmological models in which dark matter feels a fifth force
mediated by the dark energy scalar field, also known as coupled dark energy.
Our interest resides in estimating forecasts for future surveys like Euclid
when we take into account non-linear effects, relying on new fitting functions
that reproduce the non-linear matter power spectrum obtained from N-body
simulations. We obtain fitting functions for models in which the dark
matter-dark energy coupling is constant. Their validity is demonstrated for all
available simulations in the redshift range $z=0-1.6$ and wave modes below
$k=10 \text{h/Mpc}$. These fitting formulas can be used to test the predictions
of the model in the non-linear regime without the need for additional
computing-intensive N-body simulations. We then use these fitting functions to
perform forecasts on the constraining power that future galaxy-redshift surveys
like Euclid will have on the coupling parameter, using the Fisher matrix method
for galaxy clustering (GC) and weak lensing (WL). We find that by using
information in the non-linear power spectrum, and combining the GC and WL
probes, we can constrain the dark matter-dark energy coupling constant squared,
$\beta^{2}$, with precision smaller than 4\% and all other cosmological
parameters better than 1\%, which is a considerable improvement of more than an
order of magnitude compared to corresponding linear power spectrum forecasts
with the same survey specifications.
