Modeling Error and Adaptivity in Nonlinear Continuum Mechanics

Abstract

In this report, computable global bounds on errors due to the use of various mathematical models of physical phenomena are derived. The procedure involves identifying a so-called fine model among a class of models of certain events and then using that model as a datum with respect to which coarser models can be compared. The error inherent in a coarse model, compared to the fine datum, can be bounded by residual functionals unambiguously defined by solutions of the coarse model. Whenever there exist hierarchical classes of models in which levels of sophistication of various coarse models can be defined, an adaptive modeling strategy can be implemented to control modeling error. In the present work, the class of models is within those embodied in nonlinear continuum mechanics