"Estimating and Control of Modeling Error: a systematic approach to multiscale modeling of large molecular and continuum systems"

Summary We have developed a general and rigorous approach of a posteriori error estimation of both modeling and discretization errors for general nonlinear problems. The approach is based on the idea of the existence of a base model, which is used as the datum with respect to which all other models of a given class, such as those involving coarser scales, or coarser discretizations, can be measured. The method allows the estimation of errors with respect to local quantities of interest. Once a modeling error is estimated, it can be systematically reduced through the implementation of the GOALS algorithm. We have demonstrated that these methods provide a rigorous and systematic approach to multi-scale modeling and are currently extending the technique to the analysis of very large-scale models of polymer materials.