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

2014/10/13 by Lucas Chesnel, Xavier Claeys, Chesnel, Lucas +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1410.3508

openalex publication_date 2014/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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