Asymptotic expansions and effective boundary conditions: a short review for smooth and nonsmooth geometries with thin layers★
Problems involving materials with thin layers arise in various application fields. We present here the use of asymptotic expansions for linear elliptic problems to derive and justify so-called ap-proximate or effective boundary conditions. We first recall the known results of the literature, and the...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
EDP Sciences
2018-01-01
|
| Series: | ESAIM: Proceedings and Surveys |
| Online Access: | https://doi.org/10.1051/proc/201861038 |
| Summary: | Problems involving materials with thin layers arise in various application fields. We present here the use of asymptotic expansions for linear elliptic problems to derive and justify so-called ap-proximate or effective boundary conditions. We first recall the known results of the literature, and then discuss the optimality of the error estimates in the smooth case. For non-smooth geometries, the results of [18, 57] are commented and adapted to a model problem, and two improvements of the approximate model are proposed to increase its numerical performance. |
|---|---|
| ISSN: | 2267-3059 |