  Let $\varepsilon>0$ be a small parameter. We consider the domain
$\Omega_\varepsilon:=\Omega\setminus D_\varepsilon$, where $\Omega$ is an open
domain in $\mathbb{R}^n$, and $D_\varepsilon$ is a family of small balls of the
radius $d_\varepsilon=o(\varepsilon)$ distributed periodically with period
$\varepsilon$. Let $\Delta_\varepsilon$ be the Laplace operator in
$\Omega_\varepsilon$ subject to the Robin condition ${\partial u\over \partial
n}+\gamma_\varepsilon u = 0$ with $\gamma_\varepsilon\ge 0$ on the boundary of
the holes and the Dirichlet condition on the exterior boundary. Kaizu (1985,
1989) and Brillard (1988) have shown that, under appropriate assumptions on
$d_\varepsilon$ and $\gamma_\varepsilon$, the operator $\Delta_\varepsilon$
converges in the strong resolvent sense to the sum of the Dirichlet Laplacian
in $\Omega$ and a constant potential. We improve this result deriving estimates
on the rate of convergence in terms of $L^2\to L^2$ and $L^2\to H^1$ operator
norms. As a byproduct we establish the estimate on the distance between the
spectra of the associated operators.
