  In this paper, we investigate an effective model for reactive transport in
elastically deformable perforated media. This model was derived by formal
asymptotic expansions in [25], starting from a microscopic model consisting of
a linear elasticity problem on a fixed domain, i.e. in the Lagrangian
framework, and a problem for reactive transport on the current deformed domain,
i.e. in the Eulerian framework. The effective model is of micro-macro type and
features strong non-linear couplings. Here, we prove global existence in time
and uniqueness for the effective micro-macro model under a smallness assumption
for the data of the macroscopic elasticity subproblem. Moreover, we show
numerically the convergence of microscopic solutions towards the solution of
the effective model when the scale parameter {\epsilon} > 0 becomes smaller and
smaller, and also compute the approximation error. The numerical justification
of the formally derived effective micro-macro model is particularly important,
as rigorous analytical convergence proofs or error estimates are not available
so far. Finally, we compare the effective micro-macro model with alternative,
simpler effective descriptions of transport in elastic perforated media.
