  We demonstrate that by employing the correspondence between gauge theories in
geometric and in deconstructed extra dimensions, it is possible to transfer the
methods for calculating finite Casimir energy densities in higher dimensions to
the four-dimensional deconstruction setup. By this means, one obtains an
unambiguous and well-defined prescription to determine finite vacuum energy
contributions of four-dimensional quantum fields which have a
higher-dimensional correspondence. Thereby, large kink masses lead to an
exponentially suppressed Casimir effect. For a specific model we hence arrive
at a small and positive contribution to the cosmological constant in agreement
with observations.
