Dimension Reduction and Error Estimates

Merzougui, Louiza

doi:10.1177/09217134251356902

Dimension Reduction and Error Estimates

2026-05-01

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AI

DOI：10.1177/09217134251356902

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The aim of this article 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 Omega delta & esdot; O x omega delta subset of R m x R n , m , n >= 1 where omega delta = delta omega when delta -> 0 (the thickness of Omega delta is of order delta while its diameter is of order 1). The limit problem is elliptic and is posed in O . Under the assumptions that O has a smooth boundary ( C 1 , 1 ) and homogeneous Dirichlet boundary condition, we give two important results, first an estimate of the global error (of order delta 1 / 2 ), and then an estimate of the L 2 global and H 1 interior errors (of order delta ).

Keywords:

dimension reduction

error estimates

Dimension Reduction and Error Estimates

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