  We consider elliptic problems with complicated, discontinuous diffusion
tensor $A_{\scriptscriptstyle 0} $. One of the standard approaches to
numerically treat such problems is to simplify the coefficient by some
approximation, say $A_{\varepsilon}$, and to use standard finite elements. In
\cite{Repin2012} a combined modelling-discretization strategy has been proposed
which estimates the discretization and modelling errors by a posteriori
estimates of functional type. This strategy allows to balance these two errors
in a problem adapted way. However, the estimate of the modelling error is
derived under the assumption that the difference $A_{\scriptscriptstyle 0}
-A_{\varepsilon}$ is bounded in the $L^{\infty}$-norm, which requires that the
approximation of the coefficient matches the discontinuities of the original
coefficient. Therefore this theory is not appropriate for applications with
discontinuous coefficients along \textit{complicated, curved} interfaces. Based
on bounds for $A_{\scriptscriptstyle 0} -A_{\varepsilon}$ in an $L^{q}$-norm
with $q<\infty$ we generalize the combined modelling-discretization strategy to
a larger class of coefficients.
