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Mathematical Models and Methods in Applied Sciences fc World Scientific Publishing Company
 

Summary: Mathematical Models and Methods in Applied Sciences
fc World Scientific Publishing Company
Asymptotic Estimates of Hierarchical Modeling
Douglas N. Arnold
Institute for Mathematics and its Applications, University of Minnesota,
Minneapolis, MN 55455, USA
Alexandre L. Madureira
Laborat´orio Nacional de Computa¸c~ao Cient´ifica,
Petr´opolis, RJ 25651-070, Brazil
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).
1. Introduction
Much investigation has been done in the recent and not so recent past to take
advantage of the small thickness to solve or approximate elliptic problems in thin
domains. Indeed it is tempting to use dimension reduction, i.e., to pose and solve a

  

Source: Arnold, Douglas N. - School of Mathematics, University of Minnesota
Institute for Mathematics and its Applications

 

Collections: Mathematics