Title:         Asymptotic estimates of hierarchical modeling

Authors:       Douglas N. Arnold and Alexandre L. Madureira

Source:        Mathematical Models and Methods in Applied Sciences (M3AS) 13 (2003)

Status:        Published

Abstract:      In this paper we propose a way to analyze certain classes
of dimension  reduction models for elliptic problems in thin domains. 
We develop asymptotic expansions for the exact and model solutions, 
having the thickness as small parameter.  The modeling error is then
estimated by comparing the respective expansions, and the upper bounds
obtained make clear the influence  of the order of the model and the
thickness on the convergence rates.  The techniques developed here
allows for estimates in several norms and  semi-norms, and also
interior estimates (which disregards boundary layers).

Keywords:      hierarchical modeling, dimension reduction, asymptotic estimates

Subj. class.:  35C20

URL:           http://ima.umn.edu/~arnold/papers/hierarchical.pdf