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

Lucas Chesnel 1, 2, * Xavier Claeys 3, 4
* Corresponding author
1 DeFI - Shape reconstruction and identification
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
4 ALPINES - Algorithms and parallel tools for integrated numerical simulations
Inria de Paris, Institut National des Sciences Mathématiques et de leurs Interactions, LJLL - Laboratoire Jacques-Louis Lions
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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Submitted on : Tuesday, January 5, 2016 - 6:18:20 PM
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  • HAL Id : hal-01109552, version 2
  • ARXIV : 1410.3508

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Lucas Chesnel, Xavier Claeys. A numerical approach for the Poisson equation in a planar domain with a small inclusion. BIT Numerical Mathematics, Springer Verlag, 2016. ⟨hal-01109552v2⟩

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