A numerical approach for the Poisson equation in a planar domain with a small inclusion

Lucas Chesnel 1, 2 Xavier Claeys 3, 4
2 DeFI - Shape reconstruction and identification
Inria Saclay - Ile de France, CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
3 ALPINES - Algorithms and parallel tools for integrated numerical simulations
LJLL - Laboratoire Jacques-Louis Lions, Inria Paris-Rocquencourt, INSMI - Institut National des Sciences Mathématiques et de leurs Interactions
Abstract : We consider the Poisson equation in a domain with a small hole of size δ. We present a simple numerical method, based on an asymptotic analysis, which allows to approximate robustly the far field of the solution as δ goes to zero without meshing the small hole. We prove the stability of the scheme and provide error estimates. We end the paper with numerical experiments illustrating the efficiency of the technique.
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Contributor : Lucas Chesnel <>
Submitted on : Monday, January 26, 2015 - 5:04:38 PM
Last modification on : Friday, September 20, 2019 - 4:34:04 PM
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  • HAL Id : hal-01109552, version 1
  • ARXIV : 1410.3508



Lucas Chesnel, Xavier Claeys. A numerical approach for the Poisson equation in a planar domain with a small inclusion. 2014. ⟨hal-01109552v1⟩



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