  Let $\Delta_{\Omega_\varepsilon}$ be the Dirichlet Laplacian in the domain
$\Omega_\varepsilon:=\Omega\setminus\left(\cup_i D_{i \varepsilon}\right)$.
Here $\Omega\subset\mathbb{R}^n$ and $\{D_{i \varepsilon}\}_{i}$ is a family of
tiny identical holes ("ice pieces") distributed periodically in $\mathbb{R}^n$
with period $\varepsilon$. We denote by $\mathrm{cap}(D_{i \varepsilon})$ the
capacity of a single hole. It was known for a long time that
$-\Delta_{\Omega_\varepsilon}$ converges to the operator $-\Delta_{\Omega}+q$
in strong resolvent sense provided the limit $q:=\lim_{\varepsilon\to 0}
\mathrm{cap}(D_{i\varepsilon}) \varepsilon^{-n}$ exists and is finite. In the
current contribution we improve this result deriving estimates for the rate of
convergence in terms of operator norms. As an application, we establish the
uniform convergence of the corresponding semi-groups and (for bounded $\Omega$)
an estimate for the difference of the $k$-th eigenvalue of
$-\Delta_{\Omega_\varepsilon}$ and $-\Delta_{\Omega_\varepsilon}+q$. Our proofs
relies on an abstract scheme for studying the convergence of operators in
varying Hilbert spaces developed previously by the second author.
