Asymptotic estimates of hierarchical modeling

Douglas N. Arnold, Alexandre L. Madureira

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


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).

Original languageEnglish (US)
Pages (from-to)1325-1350
Number of pages26
JournalMathematical Models and Methods in Applied Sciences
Issue number9
StatePublished - Sep 2003

Bibliographical note

Funding Information:
The first author was supported by NSF grant DMS-0107233. The second author had support from CNPq-Brazil.


  • Dimension reduction
  • Hierarchical modeling
  • Plate


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