A numerical approach for the Poisson equation in a planar domain with a small inclusion
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- 作者：Lucas Chesnel ; Xavier Claeys
- 关键词：Small inclusion ; Matched asymptotics ; Singular perturbation ; Finite elements
- 刊名：BIT Numerical Mathematics
- 出版年：2016
- 出版时间：December 2016
- 年：2016
- 卷：56
- 期：4
- 页码：1237-1256
- 全文大小：
- 刊物类别：Mathematics and Statistics
- 刊物主题：Computational Mathematics and Numerical Analysis; Numeric Computing; Mathematics, general;
- 出版者：Springer Netherlands
- ISSN：1572-9125
- 卷排序：56
文摘
We consider the Poisson equation in a domain with a small inclusion. We present a simple numerical method, based on asymptotic analysis, which allows to approximate robustly the far field of the solution as the size of the inclusion goes to zero without any mesh adaptation procedure. The discretization is based on a fully standard Galerkin approach such as finite elements. We prove stability and consistency of the numerical method and provide error estimates. We end the paper with numerical experiments illustrating the efficiency of the technique.