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We consider elliptic problems with complicated, discontinuous diffusiontensor $A_{\scriptscriptstyle 0} $. One of the standard approaches tonumerically treat such problems is to simplify the coefficient by someapproximation, say $A_{\varepsilon}$, and to use standard finite elements. In\cite{Repin2012} a combined modelling-discretization strategy has been proposedwhich estimates the discretization and modelling errors by a posterioriestimates of functional type. This strategy allows to balance these two errorsin a problem adapted way. However, the estimate of the modelling error isderived under the assumption that the difference $A_{\scriptscriptstyle 0}-A_{\varepsilon}$ is bounded in the $L^{\infty}$-norm, which requires that theapproximation of the coefficient matches the discontinuities of the originalcoefficient. Therefore this theory is not appropriate for applications withdiscontinuous coefficients along \textit{complicated, curved} interfaces. Basedon bounds for $A_{\scriptscriptstyle 0} -A_{\varepsilon}$ in an $L^{q}$-normwith $q<\infty$ we generalize the combined modelling-discretization strategy toa larger class of coefficients.

A Posteriori Modelling-Discretization Error Estimate for Elliptic Problems with L ^\infty -Coefficients