HIERARCHICAL MODELING BASED ON MIXED PRINCIPLES: ASYMPTOTIC ERROR ESTIMATES

Abstract

We analyze approximation properties of dimension reduction models that are based on mixed principles. The problems of interest are elliptic PDEs in thin domains. The goal is to obtain estimates that take into account both the thickness of the domain and the order of the model. The techniques involved do not require the models to be energy minimizers, and are based on asymptotic expansions for the exact and model solutions. We obtain estimates in several norms and semi-norms, and also interior estimates (which disregards boundary layers).