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 language||English (US)|
|Number of pages||26|
|Journal||Mathematical Models and Methods in Applied Sciences|
|State||Published - Sep 2003|
Bibliographical noteFunding Information:
The first author was supported by NSF grant DMS-0107233. The second author had support from CNPq-Brazil.
- Dimension reduction
- Hierarchical modeling