Local error estimation for dimensionally reduced models of elliptic boundary value problems Original Research Article

In this paper, we present an approach to the local estimation of errors in dimensionally reduced models of elliptic boundary value problems posed on thin domains. In this approach, errors are measured in quantities of interest whose computation is typically the goal of the analysis. Explicit bounds and estimates are derived for errors in quantities characterized by continuous linear functionals. A representative numerical example showing the accuracy of the bounds and estimates is also presented.