  We present a localized a-posteriori error estimate for the localized reduced
basis multi-scale (LRBMS) method [Albrecht, Haasdonk, Kaulmann, Ohlberger
(2012): The localized reduced basis multiscale method]. The LRBMS is a
combination of numerical multi-scale methods and model reduction using reduced
basis methods to efficiently reduce the computational complexity of parametric
multi-scale problems with respect to the multi-scale parameter $\varepsilon$
and the online parameter $\mu$ simultaneously. We formulate the LRBMS based on
a generalization of the SWIPDG discretization presented in [Ern, Stephansen,
Vohralik (2010): Guaranteed and robust discontinuous Galerkin a posteriori
error estimates for convection-diffusion-reaction problems] on a coarse
partition of the domain that allows for any suitable discretization on the fine
triangulation inside each coarse grid element. The estimator is based on the
idea of a conforming reconstruction of the discrete diffusive flux, that can be
computed using local information only. It is offline/online decomposable and
can thus be efficiently used in the context of model reduction.
