Dimension reduction and error estimates
Résumé
The aim of this paper is twofold: to provide asymptotic behavior and error estimates results for an elliptic dimension reduction problem. The problem is posed in a bounded and thin domain
where ω δ = δω when δ → 0 (the thickness of Ω δ is of order δ while its diameter is of order 1). The limit problem is elliptic and is posed in O. Under the assumption that O has a smooth boundary (C 1,1 ) and homogeneous Dirichlet boundary condition, we give two important results: an estimate of the global error, whose order is δ 1/2 , and an estimate of the L 2 global and H 1 interior errors, whose order is δ.
Domaines
Mathématiques [math]Origine | Fichiers produits par l'(les) auteur(s) |
---|