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Pré-Publication, Document De Travail Année : 2023

A multi-scale patch approximation for Poisson problems with a small inhomogeneous inclusion

Résumé

The paper deals with the multi-scale approximation of the influence of a small inhomogeneity of arbitrary shape in an elastic medium. A new multi-scale patch method is introduced, whose caracteristic is to deal with a large scale problem without inclusion, a small-scale problem on a patch surrounding the inclusion defining a corrector and an iterative procedure between these two problems. Theoretical results of convergence of the iterations, a posteriori error estimate and comparison of the corrector with the asymptotic expansion are provided. The finite element approximation is also addressed together with some numerical tests.
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hal-04348250 , version 1 (16-12-2023)

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Copyright (Tous droits réservés)

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  • HAL Id : hal-04348250 , version 1

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Saber Amdouni, Mohamed Khaled Gdoura, Arnaud Heibig, Thomas Homolle, Nidhal Mannai, et al.. A multi-scale patch approximation for Poisson problems with a small inhomogeneous inclusion. 2023. ⟨hal-04348250⟩
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